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प्रश्न
Factorise by splitting the middle term to get two perfect squares.
a4 – 7a2b2 + b4
बेरीज
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उत्तर
Given expression: a4 – 7a2b2 + b4
Now, using middle term factorisation method,
a4 – 7a2b2 + b4
= a4 + 2a2b2 – 9a2b2 + b4
= a4 + 2a2b2 + b4 – 9a2b2
= (a2 + b2)2 – (3ab)2 ...[∵ (a + b)2 = a2 + 2ab + b2]
= (a2 + b2 + 3ab) (a2 + b2 – 3ab) ...[∵ a2 – b2 = (a + b) (a – b)]
The factorisation result is (a2 + b2 + 3ab) (a2 + b2 – 3ab).
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