Factorize(i) 100 (x + y )2 – 81 (a + b)2(ii) (x + 1)2 – (x – 2

1.	Factorize(i) 100 (x + y )2 – 81 (a + b)2(ii) (x + 1)2 – (x – 2)2
Answer» (i) 100 (x + y)² – 81 (a + b)² = {10 (x + y)}² – {(a (a + b)}² = {10 (x + y) + 9 (a + b)} {10 (x + y) – 9(a + b)} = (10x + 10y + 9a – 9b)} (10x + 10y – 9a – 9b) (ii) (x – 1)² – (x – 2)² = {(x – 1 +(x – 2)} {(x – 1) – (x – 2)} = (2x – 3) – (x – 1 – x + 2) = (2x – 3) × 1 = 2x – 3

Factorize(i) 100 (x + y )2 – 81 (a + b)2(ii) (x + 1)2 – (x – 2)2

Answer»

(i) 100 (x + y)² – 81 (a + b)²

= {10 (x + y)}² – {(a (a + b)}²

= {10 (x + y) + 9 (a + b)} {10 (x + y) – 9(a + b)}

= (10x + 10y + 9a – 9b)} (10x + 10y – 9a – 9b)

(ii) (x – 1)² – (x – 2)²

= {(x – 1 +(x – 2)} {(x – 1) – (x – 2)}

= (2x – 3) – (x – 1 – x + 2)

= (2x – 3) × 1 = 2x – 3