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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Refine

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

Expand

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

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

Expand

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

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

(16 cos (4 θ)) cos (θ)

(\frac{d}{d x} (3 x))^{2}

2 - 8 - 2 x - x^{2}

5 + (4 x^{3})

(x + 2) - x^{2}

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)