What is (x^5-a^5)/(x-a) ?

The solution to (x^5-a^5)/(x-a) is x^4+x^3a+x^2a^2+xa^3+a^4

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simplify (x^5-a^5)/(x-a)

simplify

\frac{x ^{5} - a ^{5}}{x - a}

x^{4} + x^{3} a + x^{2} a^{2} + x a^{3} + a^{4}

Solution steps

\frac{x ^{5} - a ^{5}}{x - a}

Apply factoring rule:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

x^{5} - a^{5} = (x - a) (x^{4} + x^{3} a + x^{2} a^{2} + x a^{3} + a^{4})

= \frac{( x - a ) ( x ^{4} + x ^{3} a + x ^{2} a ^{2} + x a ^{3} + a ^{4} )}{x - a}

Cancel the common factor:

x - a

= x^{4} + x^{3} a + x^{2} a^{2} + x a^{3} + a^{4}

- 3 v (- 8 u^{2} - 8 uv - 7 v^{2})

(- 11 - 10 i) - (- 1 + i)

\frac{3 + 7 i}{3 - 7 i}

\frac{4 x}{5} - \frac{x}{10}

6 [x - \frac{1}{2} (x - 1)]

What is (x^5-a^5)/(x-a) ?
The solution to (x^5-a^5)/(x-a) is x^4+x^3a+x^2a^2+xa^3+a^4