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## How to do Factorisation when a Binomial is a Common Factor?

1. Factorize the following binomials

(i) 3x + 21

(ii) 7a – 14

(iii) b^{3} + 3b

(iv) 20a + 5a^{2
}(v) – 16m + 20m^{3
}(vi) 5a^{2}b + 15ab^{2
}(vii) 9m^{2} + 5m

(viii) 19x – 57y

(ix) 25x^{2}y^{2}z^{3} – 15xy^{3}z

## Solution:

(i) The given expression is 3x + 21

Here, the first term is 3x and the second term is 21

By comparing the above two terms, we can observe the greatest common factor and that is 3

Now, factor out the greatest common factor from the expression

That is, 3 [x + 7]

3 [x + 7]

Therefore, the resultant value for the expression 3x + 21 is 3 [x + 7]

(ii) The given expression is 7a – 14

Here, the first term is 7a and the second term is 14

By comparing the above two terms, we can observe the greatest common factor and that is 7

Now, factor out the greatest common factor from the expression

That is, 7 [a – 2]

7 [a – 2]

Therefore, the resultant value for the expression 7a – 14 is 7 [a – 2]

(iii) The given expression is b^{3} + 3b

Here, the first term is b^{3} and the second term is 3b

By comparing the above two terms, we can observe the greatest common factor and that is b

Now, factor out the greatest common factor from the expression

That is, b [b² + 3]

b [b² + 3]

Therefore, the resultant value for the expression b^{3} + 3b is b [b² + 3]

(iv) The given expression is 20a + 5a^{2}

Here, the first term is 20a and the second term is 5a^{2}

By comparing the above two terms, we can observe the greatest common factor and that is 5a

Now, factor out the greatest common factor from the expression

That is, 5a [4 + a]

5a [4 + a]

Therefore, the resultant value for the expression 20a + 5a^{2} is 5a [4 + a]

(v) The given expression is – 16m + 20m^{3}

Here, the first term is – 16m, and the second term is 20m^{3}

By comparing the above two terms, we can observe the greatest common factor and that is 4m

Now, factor out the greatest common factor from the expression

That is, 4m [-4 + 5m²]

4m [-4 + 5m²]

Therefore, the resultant value for the expression – 16m + 20m^{3} is 4m [-4 + 5m²]

(vi) The given expression is 5a^{2}b + 15ab^{2}

Here, the first term is 5a^{2}b and the second term is 15ab^{2}

By comparing the above two terms, we can observe the greatest common factor and that is 5ab

Now, factor out the greatest common factor from the expression

That is, 5ab [a + 3b]

5ab [a + 3b]

Therefore, the resultant value for the expression 5a^{2}b + 15ab^{2} is 5ab [a + 3b]

(vii) The given expression is 9m^{2} + 5m

Here, the first term is 9m^{2} and the second term is 5m

By comparing the above two terms, we can observe the greatest common factor and that is m

Now, factor out the greatest common factor from the expression

That is, m [9m + 5]

m [9m + 5]

Therefore, the resultant value for the expression 9m^{2} + 5m is m [9m + 5]

(viii) The given expression is 19x – 57y

Here, the first term is 19x and the second term is – 57y

By comparing the above two terms, we can observe the greatest common factor and that is 19

Now, factor out the greatest common factor from the expression

That is, 19 [x – 3y]

19 [x – 3y]

Therefore, the resultant value for the expression 19x – 57y is 19 [x – 3y]

(ix) The given expression is 25x^{2}y^{2}z^{3} – 15xy^{3}z

Here, the first term is 25x^{2}y^{2}z^{3} and the second term is – 15xy^{3}z

By comparing the above two terms, we can observe the greatest common factor and that is 5xy^{2}z

Now, factor out the greatest common factor from the expression

That is, 5xy^{2}z [5xz^{2} – 3y]

5xy^{2}z [5xz^{2} – 3y]

Therefore, the resultant value for the expression 25x^{2}y^{2}z^{3} – 15xy^{3}z is 5xy^{2}z [5xz^{2} – 3y]

2. Factor each of the following algebraic expression

(i) 13x + 39

(ii) 19a – 57b

(iii) 21ab + 49abc

(iv) – 16x + 20x^{3
}(v) 12a^{2}b – 42abc

(vi) 27m^{3}n^{3} + 36m^{4}n^{2}

## Solution:

(i) The given expression is 13x + 39

Here, the first term is 13x and the second term is 39

By comparing the above two terms, we can observe the greatest common factor and that is 13

Now, factor out the greatest common factor from the expression

That is, 13 [x + 3]

13 [x + 3]

Therefore, the resultant value for the expression 13x + 39 is 13 [x + 3]

(ii) The given expression is 19a – 57b

Here, the first term is 19a and the second term is – 57b

By comparing the above two terms, we can observe the greatest common factor and that is 19

Now, factor out the greatest common factor from the expression

That is, 19 [a – 3b]

19 [a – 3b]

Therefore, the resultant value for the expression 19a – 57b is 19 [a – 3b]

(iii) The given expression is 21ab + 49abc

Here, the first term is 21ab and the second term is 49abc

By comparing the above two terms, we can observe the greatest common factor and that is 7ab

Now, factor out the greatest common factor from the expression

That is, 7ab [3 + 7c]

7ab [3 + 7c]

Therefore, the resultant value for the expression 21ab + 49abc is 7ab [3 + 7c]

(iv) The given expression is – 16x + 20x^{3}

Here, the first term is – 16x and the second term is 20x^{3}

By comparing the above two terms, we can observe the greatest common factor and that is 4x

Now, factor out the greatest common factor from the expression

That is, 4x [-4 + 5x²]

4x [-4 + 5x²]

Therefore, the resultant value for the expression – 16x + 20x^{3} is 4x [-4 + 5x²]

(v) The given expression is 12a^{2}b – 42abc

Here, the first term is 12a^{2}b and the second term is – 42abc

By comparing the above two terms, we can observe the greatest common factor and that is 6ab

Now, factor out the greatest common factor from the expression

That is, 6ab [2a – 7bc]

6ab [2a – 7bc]

Therefore, the resultant value for the expression 12a^{2}b – 42abc is 6ab [2a – 7bc]

(vi) The given expression is 27m^{3}n^{3} + 36m^{4}n^{2}

Here, the first term is 27m^{3}n^{3} and the second term is 36m^{4}n^{2}

By comparing the above two terms, we can observe the greatest common factor and that is 9m^{3}n^{2}

Now, factor out the greatest common factor from the expression

That is, 9m^{3}n^{2} [3n + 4m]

9m^{3}n^{2} [3n + 4m]

Therefore, the resultant value for the expression 27m^{3}n^{3} + 36m^{4}n^{2} is 9m^{3}n^{2} [3n + 4m]