(x-y)³-8x³ factorise
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Answer:
By using the identity,
a³ - b³ = (a - b) (a²+ b² +ab)
( x-y) ³ - 8x³
= (x-y) ³ - (2x)³
= (x - y - 2x) {(x-y)² +(2x)² +(x-y) 2x}
= ( - x - y) (x² +y² - 2xy + 4x² +2x² - 2xy)
= (-x - y) (7x² +y² - 4xy)
= -1(x+y) (7x² + y² - 4xy)
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