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Question
Factorise p4 + q4 + p2q2.
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Solution
We have, p4 + q4 + p2q2
= p4 + q4 + 2p2q2 – 2p2q2 + p2q2 ...[Adding and subtracting 2p2q2]
= p4 + q4 + 2p2q2 – p2q2
= [(p2)2 + (q2)2 + 2p2q2] – p2q2 ...[Using the identity, a2 + b2 + 2ab = (a + b)2]
= (p2 + q2)2 – (pq)2
= (p2 + q2 + pq)(p2 + q2 – pq) ...[Using the identity, a2 – b2 = (a + b)(a – b)]
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