What is (x^2+1)^3+(y^2-1)^3 ?

The solution to (x^2+1)^3+(y^2-1)^3 is x^6+y^6+3x^4-3y^4+3x^2+3y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x^2+1)^3+(y^2-1)^3

simplify

(x^{2} + 1)^{3} + (y^{2} - 1)^{3}

x^{6} + y^{6} + 3 x^{4} - 3 y^{4} + 3 x^{2} + 3 y^{2}

Solution steps

(x^{2} + 1)^{3} + (y^{2} - 1)^{3}

Expand

(x^{2} + 1)^{3} : x^{6} + 3 x^{4} + 3 x^{2} + 1

= x^{6} + 3 x^{4} + 3 x^{2} + 1 + (y^{2} - 1)^{3}

Expand

(y^{2} - 1)^{3} : y^{6} - 3 y^{4} + 3 y^{2} - 1

= x^{6} + 3 x^{4} + 3 x^{2} + 1 + y^{6} - 3 y^{4} + 3 y^{2} - 1

Group like terms

= x^{6} + y^{6} + 3 x^{4} - 3 y^{4} + 3 x^{2} + 3 y^{2} + 1 - 1

Subtract the numbers:

1 - 1 = 0

= x^{6} + y^{6} + 3 x^{4} - 3 y^{4} + 3 x^{2} + 3 y^{2}

\frac{1 x ^{1}}{6}

x^{3} - 12 x (x - 4) - 64

x^{2} + 2 2 x - 6

(6 x + 5 y)^{3} - (6 x - 5 y)^{3}

cos (x) sin^{2} (x) + cos^{3} (x)

What is (x^2+1)^3+(y^2-1)^3 ?
The solution to (x^2+1)^3+(y^2-1)^3 is x^6+y^6+3x^4-3y^4+3x^2+3y^2