Question

Factorise:

(i) (p² – 2pq + q²) – r²

(ii) (x + y)² – (x – y)²

[1 mark + 2 marks = 3 marks]

Answer 1

(i) (p² – 2pq + q²) – r²

= (p – q)² – (r)² [∵ p² – 2pq + q² = (p – q)²]
(0.5 marks)

= (p – q + r) (p – q – r)
(0.5 marks)

(ii) (x + y)² – (x – y)²

It is in the form of a² – b²

a = x + y, b = x – y

∴ a² – b² =(a + b)(a – b)
(0.5 marks)

= (x + y + x – y) [x + y – (x – y)]
(0.5 marks)

= 2x [x + y – x + y]
(0.5 marks)

= (2x) (2y) = 4xy
(0.5 marks)