Question

The factorisation of (x-y)3+8(x+y)3 is​

Answer 1

Answer:

this is the answer of this question

Answer 2

Answer:

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

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

$a {}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab)$

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

$(3x + y)( {x}^{2} - 2xy + {y}^{2} + {2x}^{2} + 8xy + 4 {y}^{2} - {2x}^{2} - {2y}^{2} )$

$(3x + y)(x {}^{2} + 2 {x}^{2} - 2 {x}^{2} + {y}^{2} + {4y}^{2} - {2y}^{2} - 2xy + 8xy)$

$(3x + y)(x {}^{2} + 3 {y}^{2} + 6xy)$

$(3x + y)(x + 3y)(x + 3y)$

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