Question

factorise (x-y) cube - 8x cube​

Answer 1

Explanation:

$(x-y)^{3} - 8x^{3}$

$= (x-y)^{3} - (2x)^3$

$= a^3 - b^3$ (Let x - y be a, 2x be b)

$= (a-b)(a^2 + ab + b^2)$      

$= (x - y - 2x)[(x-y)^2 + (x-y)(2x) + (2x)^2]$

$= (-x-y)(x^{2} - 2xy + y^2 + 2x^2 - 2xy + 4x^2)$

$= -(x+y)(7x^2 - 4xy + y^2)$

Answer: -(x + y)(7x^2 - 4xy + y^2)

I hope this helps. :D