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

The solution to factor (x+y)^3+(x-y)^3 is 2x(x^2+3y^2)

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

factor

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

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

Solution steps

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

Apply Sum of Cubes Formula:

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

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

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

Refine

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

Expand

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

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

2 e - 2

a x - 3 b x + 3 a y - 9 b y

e^{2} - 4 e + 4

ab + b c + x a + x c

e^{a t} u (t)

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