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

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

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simplify (x^4-a^4)/(x-a)

simplify

\frac{x ^{4} - a ^{4}}{x - a}

(x^{2} + a^{2}) (x + a)

Solution steps

\frac{x ^{4} - a ^{4}}{x - a}

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

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

= \frac{( x ^{2} ) ^{2} - ( a ^{2} ) ^{2}}{x - a}

Apply Difference of Two Squares Formula:

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Cancel the common factor:

x - a

= (x^{2} + a^{2}) (x + a)

(3 x + 4) (3 x - 4)

\frac{1}{( \frac{2}{x} + 4 ) - 4}

- \frac{1}{6}

(\frac{1}{4})^{- 1} + 8^{0} + 5^{2}

2 4^{2}