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Question
Use the formula to expand:
(3) (2p + m – 4n)2
(3) (2p + m – 4n)2
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Solution
We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.
Comparing (2p + m – 4n)2 with (a + b + c)2 , we get:
a = 2p, b = m and c = –4n
Substituting these in the above formula:
(2p + m – 4n)2 = (2p)2 + m2 + (–4n)2 + 2 × 2p × m + 2 × m × (–4n) + 2 × (–4n) × 2p
= 4p2 + m2 + 16n2 + 4pm – 8mn – 16pn
Comparing (2p + m – 4n)2 with (a + b + c)2 , we get:
a = 2p, b = m and c = –4n
Substituting these in the above formula:
(2p + m – 4n)2 = (2p)2 + m2 + (–4n)2 + 2 × 2p × m + 2 × m × (–4n) + 2 × (–4n) × 2p
= 4p2 + m2 + 16n2 + 4pm – 8mn – 16pn
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