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Question
Factorise by splitting the middle term to get two perfect squares.
a4 + 2a2b2 + 9b4
Sum
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Solution
Given expression: a4 + 2a2b2 + 9b4
Now, using middle term factorisation method,
a4 + 2a2b2 + 9b4
= a4 + 6a2b2 – 4a2b2 + 9b4
= a4 + 6a2b2 + 9b4 – 4a2b2
= (a2 + 3)2 – (2ab)2 ...[∵ (a + b)2 = a2 + 2ab + b2]
= (a2 + 3 + 2ab) (a2 + 3 – 2ab) ...[∵ a2 – b2 = (a + b) (a – b)]
The factorisation result is (a2 + 3 + 2ab) (a2 + 3 – 2ab).
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