Simplify:

1. (2x-5y)cube -(2x+5y)cube

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Solution

(2x-5y)³-(2x+5y)³

=8x³-125y³-32x5y(2x-5y)-[8x³+125y³+32x5y(2x+5y)]

=8x³-125y³-32x5y(2x-5y)-8x³-125y³-32x5y(2x+5y)]

=-250y³-60x²y+150xy²-60x²y-150xy²

=-250y³-120x²y

or

(a-b)³-(a+b)³=-2b³-6(a²b)

=-2(5y)³-6(2x2x5y)

=-2(125y³)-120x²y

=-250y³-120x²y

= -(250y³+120x²y)

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