What is (x^4-y^4)/(x+y) ?

The solution to (x^4-y^4)/(x+y) is (x^2+y^2)(x-y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x^4-y^4)/(x+y)

simplify

\frac{x ^{4} - y ^{4}}{x + y}

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

Solution steps

\frac{x ^{4} - y ^{4}}{x + y}

x^{4} = (x^{2})^{2}

y^{4} = (y^{2})^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Cancel the common factor:

x + y

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

(y^{2} + 2 y - 3) - (4 y^{2} - 5 y - 2)

3 \cdot 2^{- 1}

3 \cdot 2^{- 2}

4 (x - 2 y) - (2 x - 9 y)

6 \cdot 12