Question:
Simplify (2x- 5y)3 – (2x+ 5y)3.
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 x 125y3 – 30xy(4x) = -250y3 -120x2y
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