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I. Worksheet on factorization using formula when a binomial is the difference of two squares

1. a^{2} – 36

2. 4x^{2} – 9

3. 81 – 49a^{2
}4. 4a^{2} – 9b^{2
}5. 16m^{2} – 225n^{2
}6. 9a^{2}b^{2} – 25

7. 16a^{2} – ^{1}/_{144
}8. (2x + 3y)^{2} – 16z^{2
}9. 1 – (m – n)^{2
}10. 9(a + b)^{2} – a^{2
}11. 25(x + y)^{2} – 16(x – y)^{2
}12. 20x^{2} – 45y^{2
}13. a^{3} – 64a

14. 12a^{2} – 27

15. 3a^{5} – 48a^{3
}16. 63x^{2}y^{2} – 7

17. m^{2} – 2mn + n^{2} – r^{2
}18. a^{2} – b^{2} – 2ab – 1

19. 9a^{2} – b^{2} + 4b – 4

## Solution:

1. Given expression is a^{2} – 36^{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(a)^{2} – (6)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a and b = 6^{
}[a + 6] [a – 6]

The final answer is [a + 6] [a – 6]

2. Given expression is 4x^{2} – 9^{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(2x)^{2} – (3)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 2x and b = 3^{
}[2x + 3] [2x – 3]

The final answer is [2x + 3] [2x – 3]

3. Given expression is 81 – 49a^{2}^{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(9)^{2} – (7a)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 9 and b = 7a^{
}[9 + 7a] [9 – 7a]

The final answer is [9 + 7a] [9 – 7a]

4. Given expression is 4a^{2} – 9b^{2}^{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(2a)^{2} – (3b)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 2a and b = 3b^{
}[2a + 3b] [2a – 3b]

The final answer is [2a + 3b] [2a – 3b]

5. Given expression is 16m^{2} – 225n^{2}^{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(4m)^{2} – (15n)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 4m and b = 15n^{
}[4m + 15n] [4m – 15n]

The final answer is [4m + 15n] [4m – 15n]

6. Given expression is 9a^{2}b^{2} – 25^{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(3ab)^{2} – (5)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 3ab and b = 5^{
}[3ab + 5] [3ab – 5]

The final answer is [3ab + 5] [3ab – 5]

7. Given expression is 16a^{2} – ^{1}/_{144
}Rewrite the given expression in the form of a^{2} – b^{2}.

(4a)^{2} – (1/12)^{2
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 4a and b = 1/12^{
}[4a + 1/12] [4a – 1/12]

The final answer is [4a + 1/12] [4a – 1/12]

8. Given expression is (2x + 3y)^{2} – 16z^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(2x + 3y)^{2} – (4z)^{2}^{
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 2x + 3y and b = 4z^{
}[2x + 3y + 4z] [2x + 3y – 4z]

The final answer is [2x + 3y + 4z] [2x + 3y – 4z]

9. Given expression is 1 – (m – n)^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(1)^{2} – (m – n)^{2}^{
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 1 and b = m – n^{
}[1 + m – n] [1 – (m – n)]

[1 + m – n] [1 – m + n]

The final answer is [1 + m – n] [1 – m + n]

10. Given expression is 9(a + b)^{2} – a^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(3(a + b))^{2} – (a)^{2}^{
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 3(a + b) and b = a^{
}[3a + 3b + a] [3a + 3b – a]

[4a + 3b] [2a + 3b]

The final answer is [4a + 3b] [2a + 3b]

11. Given expression is 25(x + y)^{2} – 16(x – y)^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(5(x + y))^{2} – (4(x – y))^{2}^{
}Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 5(x + y) and b = 4(x – y)^{
}[5x + 5y + 4x – 4y] [5x + 5y – 4x + 4y]

[9x + y] [x + 9y]

The final answer is [9x + y] [x + 9y]

12. Given expression is 20x^{2} – 45y^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

5{(2x)^{2} – (3y)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 2x and b = 3y^{
}5{[2x + 3y] [2x – 3y]}

The final answer is 5{[2x + 3y] [2x – 3y]}

13. Given expression is a^{3} – 64a_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

a{(a)^{2} – (8)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a and b = 8^{
}a{[a + 8] [a – 8]}

The final answer is a{[a + 8] [a – 8]}

14. Given expression is 12a^{2} – 27_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

3{(2a)^{2} – (3)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 2a and b = 3^{
}3{[2a + 3] [2a – 3]}

The final answer is 3{[2a + 3] [2a – 3]}

15. Given expression is 3a^{5} – 48a^{3}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

3a^{3}{(a)^{2} – (4)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a and b = 4^{
}3a^{3}{[a + 4] [a – 4]}

The final answer is 3a^{3}{[a + 4] [a – 4]}

16. Given expression is 63x^{2}y^{2} – 7_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

7{(3xy)^{2} – (1)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 3xy and b = 1^{
}7{[3xy + 1] [3xy – 1]}

The final answer is 7{[3xy + 1] [3xy – 1]}

17. Given expression is m^{2} – 2mn + n^{2} – r^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

m^{2} – 2mn + n^{2 }is in the form of a^{2} – 2ab + b^{2}

{(m – n)^{2} – (r)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = m – n and b = r^{
}{[m – n + r] [m – n – r]}

The final answer is 7{[3xy + 1] [3xy – 1]}

18. Given expression is a^{2} – b^{2} – 2ab – 1_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

a^{2} – b^{2} – 2ab^{ }is in the form of a^{2} – 2ab + b^{2}

{(a – b)^{2} – (1)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a – b and b = 1^{
}{[a – b + 1] [a – b – 1]}

The final answer is {[a – b + 1] [a – b – 1]}

19. Given expression is 9a^{2} – b^{2} + 4b – 4

9a^{2} – b^{2} + 4b – 4 = 9a^{2} – (b^{2} – 4b + 2^{2})

Rewrite the given expression in the form of a^{2} – b^{2}.

b^{2} – 4b + 2^{2}^{ }is in the form of a^{2} – 2ab + b^{2}

{(3a)^{2} – (b – 2)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 3a and b = b – 2^{
}{[3a + b – 2] [3a – b + 2]}

The final answer is {[3a + b – 2] [3a – b + 2]}

II. Solved Problems on Factorization Using Formula

1. a^{2} – 2ab + b^{2} – c^{2
}2. 25 – x^{2} – y^{2} -2xy

3. 16b^{3} – 4b

4. 3a^{5} – 48a

5. (3a – 4b)^{2} – 25c^{2
}6. (2m + 3n)^{2} – 1

7. 16z^{2} – (5x + y)^{2
}8. 100 – (a – 5)^{2
}9. Evaluate:

(i) (13)^{2} – (12)^{2
}(ii) (6.3)^{2} – (4.2)^{2}

## Solution:

1. Given expression is a^{2} – 2ab + b^{2} – c^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

a^{2} – b^{2} – 2ab^{ }is in the form of a^{2} – 2ab + b^{2}

{(a – b)^{2} – (c)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a – b and b = c^{
}{[a – b + c] [a – b – c]}

The final answer is {[a – b + c] [a – b – c]}

2. Given expression is 25 – x^{2} – y^{2} -2xy_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

25 – x^{2} – y^{2} -2xy = 25 – (x^{2} + y^{2} + 2xy)

x^{2} + y^{2} + 2xy^{ }is in the form of a^{2} + 2ab + b^{2}

{(5)^{2} – (x + y)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 5 and b = x + y^{
}{[5 + x + y] [5 – x – y]}

The final answer is {[5 + x + y] [5 – x – y]}

3. Given expression is 16b^{3} – 4b_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

b{(4b)^{2} – (2)^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 4b and b = 2^{
}b{[4b + 2] [4b – 2]}

The final answer is b{[4b + 2] [4b – 2]}

4. Given expression is 3a^{5} – 48a_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

3a{(a^{2})^{2} – (2^{2})^{2}}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a^{2} and b = 2^{2}^{
}3a{[a^{2} + 2^{2}] [a^{2} – 2^{2}]}

From the above equation, [a^{2} – 2^{2}] is in the form of a^{2} – b^{2}.

[(a)^{2} – (2)^{2}]

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = a and b = 2

[a + 2] [a – 2]^{
}Now, 3a{[a^{2} + 2^{2}] [a^{2} – 2^{2}]}

3a{[a^{2} + 4] [a + 2] [a – 2]}

The final answer is 3a{[a^{2} + 4] [a + 2] [a – 2]}

5. Given expression is (3a – 4b)^{2} – 25c^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(3a – 4b)^{2} – (5c)^{2}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 3a – 4b and b = 5c^{
}{[3a – 4b + 5c] [3a – 4b – 5c]}

The final answer is {[3a – 4b + 5c] [3a – 4b – 5c]}

6. Given expression is (2m + 3n)^{2} – 1_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(2m + 3n)^{2} – (1)^{2}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 2m + 3n and b = 1^{
}{[2m + 3n + 1] [2m + 3n – 1]}

The final answer is {[2m + 3n + 1] [2m + 3n – 1]}

7. Given expression is 16z^{2} – (5x + y)^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(4z)^{2} – (5x + y)^{2}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 4z and b = 5x + y^{
}{[4z + 5x + y] [4z – (5x + y)]}

{[4z + 5x + y] [4z – 5x – y]}

The final answer is {[4z + 5x + y] [4z – 5x – y]}

8. Given expression is 100 – (a – 5)^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(10)^{2} – (a – 5)^{2}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 10 and b = a – 5^{
}{[10 + a – 5] [10 – (a – 5)]}

{[10 + a – 5] [10 – a + 5]}

The final answer is {[10 + a – 5] [10 – a + 5]}

9. (i) Given expression is (13)^{2} – (12)^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(13)^{2} – (12)^{2}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 13 and b = 12^{
}{[13 + 12] [13 – 12)]}

{[25] [1]} = 25

The final answer is 25

9. (ii) Given expression is (6.3)^{2} – (4.2)^{2}_{
}Rewrite the given expression in the form of a^{2} – b^{2}.

(6.3)^{2} – (4.2)^{2}

Now, apply the formula of a^{2} – b^{2} = (a + b) (a – b), where a = 6.3 and b = 4.2^{
}{[6.3 + 4.2] [6.3 – 4.2)]}

{[10.5] [2.1]} = 22.05

The final answer is 22.05

III. Worksheet on factorization using formula when the given expression is a perfect square

1. a^{2} + 8a + 16

2. a^{2} + 14a + 49

3. 1 + 2a + a^{2
}4. 9 + 6c + c^{2
}5. m^{2} + 6am + 9a^{2
}6. 4a^{2} + 20a +25

7. 36a^{2} + 36a + 9

8. 9a^{2} + 24a + 16

9. a^{2} + a + 1/4

10. a^{2} – 6a + 9

## Solution:

1. Given expression is a^{2} + 8a + 16

The given expression a^{2} + 8a + 16 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = a, b = 4

Apply the formula and substitute the a and b values.

a^{2} + 8a + 16

(a)^{2} + 2 (a) (4) + (4)^{2
}(a + 4)^{2}

(a + 4) (a + 4)

Factors of the a^{2} + 8a + 16 are (a + 4) (a + 4)

2. Given expression is a^{2} + 14a + 49

The given expression a^{2} + 14a + 49 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = a, b = 7

Apply the formula and substitute the a and b values.

a^{2} + 14a + 49

(a)^{2} + 2 (a) (7) + (7)^{2
}(a + 7)^{2}

(a + 7) (a + 7)

Factors of the a^{2} + 14a + 49 are (a + 7) (a + 7)

3. Given expression is 1 + 2a + a^{2}

The given expression a^{2} + 2a + 1 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = a, b = 1

Apply the formula and substitute the a and b values.

a^{2} + 2a + 1

(a)^{2} + 2 (a) (1) + (1)^{2
}(a + 1)^{2}

(a + 1) (a + 1)

Factors of the 1 + 2a + a^{2} are (a + 1) (a + 1)

4. Given expression is 9 + 6c + c^{2}

The given expression c^{2} + 6c + 9 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = c, b = 3

Apply the formula and substitute the a and b values.

c^{2} + 6c + 9

(c)^{2} + 2 (a) (3) + (3)^{2
}(c + 3)^{2}

(c + 3) (c + 3)

Factors of the 9 + 6c + c^{2} are (c + 3) (c + 3)

5. Given expression is m^{2} + 6am + 9a^{2}

The given expression m^{2} + 6am + 9a^{2} is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = m, b = 3a

Apply the formula and substitute the a and b values.

m^{2} + 6am + 9a^{2}

(m)^{2} + 2 (m) (3a) + (3a)^{2
}(m + 3a)^{2}

(m + 3a) (m + 3a)

Factors of the m^{2} + 6am + 9a^{2} are (m + 3a) (m + 3a)

6. Given expression is 4a^{2} + 20a +25

The given expression 4a^{2} + 20a +25 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = 2a, b = 5

Apply the formula and substitute the a and b values.

4a^{2} + 20a +25

(2a)^{2} + 2 (2a) (5) + (5)^{2
}(2a + 5)^{2}

(2a + 5) (2a + 5)

Factors of the 4a^{2} + 20a +25 are (2a + 5) (2a + 5)

7. Given expression is 36a^{2} + 36a + 9

The given expression 36a^{2} + 36a + 9 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = 6a, b = 3

Apply the formula and substitute the a and b values.

36a^{2} + 36a + 9

(6a)^{2} + 2 (6a) (3) + (3)^{2
}(6a + 3)^{2}

(6a + 3) (6a + 3)

Factors of the 36a^{2} + 36a + 9 are (6a + 3) (6a + 3)

8. Given expression is 9a^{2} + 24a + 16

The given expression 9a^{2} + 24a + 16 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = 3a, b = 4

Apply the formula and substitute the a and b values.

9a^{2} + 24a + 16

(3a)^{2} + 2 (3a) (4) + (4)^{2
}(3a + 4)^{2}

(3a + 4) (3a + 4)

Factors of the 9a^{2} + 24a + 16 are (3a + 4) (3a + 4)

9. Given expression is a^{2} + a + 1/4

The given expression a^{2} + a + 1/4 is in the form a^{2} + 2ab + b^{2}.

So find the factors of given expression using a^{2} + 2ab + b^{2} = (a + b)^{2} = (a + b) (a + b) where a = a, b = 1/2

Apply the formula and substitute the a and b values.

a^{2} + a + 1/4

(a)^{2} + 2 (a) (1/2) + (1/2)^{2
}(a + 1/2)^{2}

(a + 1/2) (a + 1/2)

Factors of the a^{2} + a + 1/4 are (a + 1/2) (a + 1/2)

10. The given expression a^{2} – 6a + 9 is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = a, b = 3

Apply the formula and substitute the a and b values.

a^{2} – 6a + 9

(a)^{2} – 2 (a) (3) + (3)^{2
}(a – 3)^{2}

(a – 3) (a – 3)

Factors of the a^{2} – 6a + 9 are (a – 3) (a – 3)

IV. Solved Problems on Factorization Using Formula When the Given Expression Is a Perfect Square

1. a^{2} – 10a + 25

2. 9a^{2} – 12a + 4

3. 16a^{2} – 24a + 9

4. 1 – 2a + a^{2
}5. 1 – 6a + 9a^{2
}6. x^{2}y^{2} – 6xyz + 9z^{2
}7. a^{2} – 4ab + 4b^{2}

## Solution:

1. The given expression a^{2} – 10a + 25 is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = a, b = 5

Apply the formula and substitute the a and b values.

a^{2} – 10a + 25

(a)^{2} – 2 (a) (5) + (5)^{2
}(a – 5)^{2}

(a – 5) (a – 5)

Factors of the a^{2} – 10a + 25 are (a – 5) (a – 5)

2. The given expression 9a^{2} – 12a + 4 is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = 3a, b = 2

Apply the formula and substitute the a and b values.

9a^{2} – 12a + 4

(3a)^{2} – 2 (3a) (2) + (2)^{2
}(3a – 2)^{2}

(3a – 2) (3a – 2)

Factors of the 9a^{2} – 12a + 4 are (3a – 2) (3a – 2)

3. The given expression 16a^{2} – 24a + 9 is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = 4a, b = 3

Apply the formula and substitute the a and b values.

16a^{2} – 24a + 9

(4a)^{2} – 2 (4a) (3) + (3)^{2
}(4a – 3)^{2}

(4a – 3) (4a – 3)

Factors of the 16a^{2} – 24a + 9 are (4a – 3) (4a – 3)

4. The given expression 1 – 2a + a^{2} is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = a, b = 1

Apply the formula and substitute the a and b values.

1 – 2a + a^{2}

(a)^{2} – 2 (a) (1) + (1)^{2
}(a – 1)^{2}

(a – 1) (a – 1)

Factors of the 1 – 2a + a^{2} are (a – 1) (a – 1)

5. The given expression 1 – 6a + 9a^{2} is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = 3a, b = 1

Apply the formula and substitute the a and b values.

1 – 6a + 9a^{2}

(3a)^{2} – 2 (3a) (1) + (1)^{2
}(3a – 1)^{2}

(3a – 1) (3a – 1)

Factors of the 1 – 6a + 9a^{2} are (3a – 1) (3a – 1)

6. The given expression x^{2}y^{2} – 6xyz + 9z^{2} is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = xy, b = 3z

Apply the formula and substitute the a and b values.

x^{2}y^{2} – 6xyz + 9z^{2}

(xy)^{2} – 2 (xy) (3z) + (3z)^{2
}(xy – 3z)^{2}

(xy – 3z) (xy – 3z)

Factors of the x^{2}y^{2} – 6xyz + 9z^{2} are (xy – 3z) (xy – 3z)

7. The given expression a^{2} – 4ab + 4b^{2} is in the form a^{2} – 2ab + b^{2}.

So find the factors of given expression using a^{2} – 2ab + b^{2} = (a – b)^{2} = (a – b) (a – b) where a = a, b = 2b

Apply the formula and substitute the a and b values.

a^{2} – 4ab + 4b^{2}

(a)^{2} – 2 (a) (2b) + (2b)^{2
}(a – 2b)^{2}

(a – 2b) (a – 2b)

Factors of the a^{2} – 4ab + 4b^{2} are (a – 2b) (a – 2b)