Factorise 2(x – 2y)2 – 50y2

(i) 2(x – 2y)2 – 50y2

(ii) 32 – 2(x – 4)2

Answer :

(i) 2(x – 2y)2 – 50y2

Take out common in all terms,

2[(x – 2y)2 – 25y2]

2[(x – 2y)2 – (5y)2]

We know that, a2 – b2 = (a + b) (a – b)

2[(x – 2y + 5y) (x – 2y – 5y)]

2[(x + 3y) (x – 7y)]

2(x + 3y) (x – 7y)

(ii) 32 – 2(x – 4)2

32 – 2(x – 4)2

Take out common in all terms,

2[16 – (x – 4)2]

2[42– (x – 4)2]

We know that, a2 – b2 = (a + b) (a – b)

2[(4 + x – 4) (4 – x + 4)]

2[(x) (8 – x)]

2x (8 – x)

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