What is (x^8-y^8)/(x+y) ?

The solution to (x^8-y^8)/(x+y) is (x^4+y^4)(x^2+y^2)(x-y)

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simplify (x^8-y^8)/(x+y)

simplify

\frac{x ^{8} - y ^{8}}{x + y}

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

Solution steps

\frac{x ^{8} - y ^{8}}{x + y}

x^{8} = (x^{4})^{2}

y^{8} = (y^{4})^{2}

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

Apply Difference of Two Squares Formula:

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

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

= \frac{( x ^{4} + y ^{4} ) ( x ^{4} - y ^{4} )}{x + y}

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

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

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

Cancel the common factor:

x + y

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

\frac{12}{4} + 2 \frac{1}{2} - 3

x^{4} \cdot x^{- 4}

(1 - u^{2})^{4}

9^{\frac{1}{1}}

\frac{4}{6} - \frac{1}{6}

What is (x^8-y^8)/(x+y) ?
The solution to (x^8-y^8)/(x+y) is (x^4+y^4)(x^2+y^2)(x-y)