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Question
Simplify.
(3k − 4r − 2m)2 − (3k + 4r − 2m)2
Simplify
Solution
It is known that,
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(3k − 4r − 2m)2 − (3k + 4r − 2m)2
= [(3k)2 + (−4r)2 + (−2m)2 + 2(3k)(−4r) + 2(−4r)(−2m) + 2(−2m)(3k)] − [(3k)2 + (4r)2 + (−2m)2 + 2(3k)(4r) + 2(4r)(−2m) + 2(−2m)(3k)]
= 9k2 + 16r2 + 4m2 − 24kr + 16rm − 12km − 9k2 − 16r2 − 4m2 − 24kr + 16rm + 12km
= 9k2 − 9k2 + 16r2 − 16r2 + 4m2 − 4m2 − 24kr − 24kr + 16rm + 16rm − 12km + 12km
= 32rm − 48kr
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