What is factor (x+y)^6+(x-y)^6 ?

The solution to factor (x+y)^6+(x-y)^6 is 2(x^2+y^2)(x^4+14x^2y^2+y^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor (x+y)^6+(x-y)^6

factor

(x + y)^{6} + (x - y)^{6}

2 (x^{2} + y^{2}) (x^{4} + 14 x^{2} y^{2} + y^{4})

Solution steps

(x + y)^{6} + (x - y)^{6}

Rewrite

(x + y)^{6} + (x - y)^{6}

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

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

Apply Sum of Cubes Formula:

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

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

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

Expand

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

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

Expand

(x + y)^{4} - (x - y)^{2} (x + y)^{2} + (x - y)^{4} : x^{4} + 14 x^{2} y^{2} + y^{4}

= (2 x^{2} + 2 y^{2}) (x^{4} + 14 x^{2} y^{2} + y^{4})

Factor

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

= 2 (x^{2} + y^{2}) (x^{4} + 14 x^{2} y^{2} + y^{4})

sin (x) (cos (x))^{3} d x

\frac{d c}{d t} + 2 c

cos (h) (2 t) - sin (2 t)

400 \times 10 + 40 \times 5 + 1

5 (a)^{2} - (a) + 5

What is factor (x+y)^6+(x-y)^6 ?
The solution to factor (x+y)^6+(x-y)^6 is 2(x^2+y^2)(x^4+14x^2y^2+y^4)