Question

Factorise:75(x + y)2 - 48(x - y)2

Answer 1

75(x + y)2 - 48(x - y)2

= 3[25 (x + y)2 - 16 (x - y)2]

= 3[{5 (x + y)2} - {4 (x - y)}2]

Using a2 b2 = (a + b) (a b)

= 3 [5(x + y) + 4(x - y)] [5(x + y) - 4(x - y)]

= 3 [5x + 5y + 4x - 4y] [5x + 5y - 4x + 4y]

= 3 (9x + y) (x + 9y)