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Question
125 + 8x3 - 27 y3 + 90xy
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Solution
= 53 + (2x)3 + (-3y )3 - 3 × 5 × 2x × (-3y )
= (5 + 2x + (-3y ))(52 + (2x)2 + (-3y )2 - 5(2x) - 2x (-3y ) - (-3y )5)
= (5 + 2x - 3y )(25 + 4x2 + 9 y2 -10x + 6xy +15 y )
∴ 125 + 8x3 - 27 y3 + 90xy = (5 + 2x - 3y)(25 + 4x2 + 9 y2 -10x + 6xy +15y )
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