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

The solution to factor (x+y)^3-8(x-y)^3 is (-x+3y)(7x^2-6xy+3y^2)

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

factor

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

(- x + 3 y) (7 x^{2} - 6 x y + 3 y^{2})

Solution steps

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

Rewrite

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

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

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

x + y - 2 (x - y) : - x + 3 y

= (3 y - x) (2 (x - y) (x + y) + (x + y)^{2} + 4 (x - y)^{2})

Expand

4 (x - y)^{2} + 2 (x - y) (x + y) + (x + y)^{2} : 7 x^{2} - 6 x y + 3 y^{2}

= (3 y - x) (7 x^{2} - 6 x y + 3 y^{2})

27

18 - 3 x^{4}

(0.5 (e^{x} - e^{- x}))^{2}

8 \cdot e^{2} - e^{5}

c e^{t} - c^{2} e^{2 t}

What is factor (x+y)^3-8(x-y)^3 ?
The solution to factor (x+y)^3-8(x-y)^3 is (-x+3y)(7x^2-6xy+3y^2)