Question
Expand $(4a – 2b – 3c)^2$
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Answer
Using Identity $(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx,$ we have
$(4a – 2b – 3c)^2 = [4a + (–2b) + (–3c)]^2$
$= (4a)^2 + (–2b)^2 + (–3c)^2 + 2(4a)(–2b) + 2(–2b)(–3c) + 2(–3c)(4a)$
$= 16a^2 + 4b^2 + 9c^2 – 16ab + 12bc – 24ac$
This is the required expansion.
$(4a – 2b – 3c)^2 = [4a + (–2b) + (–3c)]^2$
$= (4a)^2 + (–2b)^2 + (–3c)^2 + 2(4a)(–2b) + 2(–2b)(–3c) + 2(–3c)(4a)$
$= 16a^2 + 4b^2 + 9c^2 – 16ab + 12bc – 24ac$
This is the required expansion.
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