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

The solution to factor 8(x+y)^3-y^3 is (2x+y)(7y^2+10xy+4x^2)

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

factor

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

(2 x + y) (7 y^{2} + 10 x y + 4 x^{2})

Solution steps

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

Rewrite

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

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

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

2 (x + y) - y : 2 x + y

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

Expand

4 (x + y)^{2} + 2 y (x + y) + y^{2} : 7 y^{2} + 10 x y + 4 x^{2}

= (2 x + y) (4 x^{2} + 10 x y + 7 y^{2})

ln (3) (3)

216 - x^{15}

(cos (8 x))^{2}

128

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

What is factor 8(x+y)^3-y^3 ?
The solution to factor 8(x+y)^3-y^3 is (2x+y)(7y^2+10xy+4x^2)