What is factor (x-y)^3+8y^3 ?

The solution to factor (x-y)^3+8y^3 is (y+x)(7y^2-4xy+x^2)

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factor (x-y)^3+8y^3

factor

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

(y + x) (7 y^{2} - 4 x y + x^{2})

Solution steps

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

Rewrite

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

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

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

Apply Sum of Cubes Formula:

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

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

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

Refine

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

Expand

(x - y)^{2} - 2 y (x - y) + 4 y^{2} : 7 y^{2} - 4 x y + x^{2}

= (x + y) (x^{2} - 4 x y + 7 y^{2})

6 f e + 2 f h + 3 g e + g h

(- 5) + 3 a

m^{24} y^{3} - n^{3} z^{24}

2 a c + 2 a d - 3 b c - 3 b d

x^{2} + 4 + 4

What is factor (x-y)^3+8y^3 ?
The solution to factor (x-y)^3+8y^3 is (y+x)(7y^2-4xy+x^2)