Question

factorise—7 (a² + b²)² - 15 (a - b) + 8 (a²-b³)²​

Answer 1

As we know that,

x2 – y2 = (x – y)(x + y)

The given expression can be rewritten as:

7(a2 + b2)2 – 15(a2 + b2)(a2 – b2) + 8 (a2 – b2)2

Let (a2 + b2) = p and (a2 – b2) = q

⇒ 7p2 – 15pq + 8q2

⇒ 7p2 – 7pq – 8pq + 8q2

⇒ 7p(p – q) – 8q(p – q)

⇒ (7p – 8q)(p – q)

On substituting the value of p and q, we get,

⇒ (7(a2 + b2) - 8(a2 – b2))( a2 + b2 – a2 + b2)

⇒ (7a2 + 7b2 – 8a2 + 8b2) (2b2)

⇒ 2b2(15b2 – a2)

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