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Question
Simplify (2x – 5y)3 – (2x + 5y)3.
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Solution
(2x – 5y)3 – (2x + 5y)3 = [(2x)3 – (5y)3 – 3(2x)(5y)(2x – 5y)] – [(2x)3 + (5y)3 + 3(2x)(5y)(2x + 5y)] ...[Using identity, (a – b)3 = a3 – b3 – 3ab and (a + b)3 = a3 + b3 + 3ab]
= (2x)3 – (5y)3 – 30xy(2x – 5y) – (2x)3 – (5y)3 – 30xy(2x + 5y)
= –2(5y)3 – 30xy(2x – 5y + 2x + 5y)
= –2 × 125y3 – 30xy(4x)
= –250y3 – 120x2y
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