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Question
Factorise:
5a2 - b2 - 4ab + 7a - 7b
Solution
5a2 - b2 - 4ab + 7a - 7b
= 4a2 + a2 - b2 - 4ab + 7a - 7b
= a2 - b2 + 4a2 - 4ab + 7a - 7b
= (a2 - b2) + 4a(a - b) + 7(a - b)
= (a - b)(a + b) + 4a(a - b) + 7(a - b) ...[∵ a2 - b2 = (a + b)(a - b)]
= (a - b)[(a + b) + 4a + 7]
= (a - b)[a + b + 4a + 7]
= (a - b)[5a + b + 7]
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