What is (x^4-625)/(x-5) ?

The solution to (x^4-625)/(x-5) is (x^2+25)(x+5)

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simplify (x^4-625)/(x-5)

simplify

\frac{x ^{4} - 625}{x - 5}

(x^{2} + 25) (x + 5)

Solution steps

\frac{x ^{4} - 625}{x - 5}

Apply exponent rules

= \frac{( x ^{2} ) ^{2} - 2 5 ^{2}}{x - 5}

Apply Difference of Two Squares Formula:

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

(x^{2})^{2} - 2 5^{2} = (x^{2} + 25) (x^{2} - 25)

= \frac{( x ^{2} + 25 ) ( x ^{2} - 25 )}{x - 5}

Factor

x^{2} - 25 : (x + 5) (x - 5)

= \frac{( x ^{2} + 25 ) ( x + 5 ) ( x - 5 )}{x - 5}

Cancel the common factor:

x - 5

= (x^{2} + 25) (x + 5)

1 4^{0}

x^{2} + 5 x - 500

(m + 4)^{3}

16 \frac{1}{3}

\frac{3}{10} + \frac{1}{8} + \frac{3}{4}