Expand the following using identities : (i) (7x + 2y)2 (ii) (4m –

1.	Expand the following using identities : (i) (7x + 2y)2 (ii) (4m – 3m)2(iii) (4a + 3b) (4a – 3b) (iv) (k + 2) (k – 3)
Answer» (i) (7x + 2y)² = (7x)² + 2 (7x) (2y) + (2y)² = 49x² + 28xy + 4y² (ii) (4m – 3m)² = (4m)² – 2(4m) (3m) + (3m)² = 16m² – 24mn + 9n² (iii) (4a + 3b) (4a – 3b) [We have (a + b) (a – b) = a² – b²] Put [a = 4a, b = 3b] (4a + 3b) (4a – 3b) = (4a)² – (3b)² = 16a² – 9b² (iv) (k + 2)(k – 3) [We have (x + a) (x – b) = x² + (a – b)x – ab] Put [x = k, a = 2, b = 3] (k + 2) (k – 3) = k² + (2 – 3)x – 2 x 3 = k² – x – 6

Expand the following using identities : (i) (7x + 2y)2 (ii) (4m – 3m)2(iii) (4a + 3b) (4a – 3b) (iv) (k + 2) (k – 3)

Answer»

(i) (7x + 2y)² = (7x)² + 2 (7x) (2y) + (2y)² = 49x² + 28xy + 4y²

(ii) (4m – 3m)² = (4m)² – 2(4m) (3m) + (3m)² = 16m² – 24mn + 9n²

(iii) (4a + 3b) (4a – 3b) [We have (a + b) (a – b) = a² – b²]

Put [a = 4a, b = 3b]

(4a + 3b) (4a – 3b) = (4a)² – (3b)² = 16a² – 9b²

(iv) (k + 2)(k – 3) [We have (x + a) (x – b) = x² + (a – b)x – ab]

Put [x = k, a = 2, b = 3]

(k + 2) (k – 3) = k² + (2 – 3)x – 2 x 3 = k² – x – 6