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

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

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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)

(- 4 i)^{3} \cdot 2 i

\frac{6 x ^{7}}{2 x ^{4}}

(3 x + y) (3 x - y)

\frac{1}{3} \times \frac{1}{3}

\frac{x}{1 - x ^{2}}