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Divide
a(5a^(2)-125) by
5a(a+5)

Divide $a\left(5 a^{2}-125\right)$ by $5 a(a+5)$

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Divide polynomials using long division

Full solution

Q. Divide

a\left(5 a^{2}-125\right)

by

5 a(a+5)

Identify Terms: Identify the terms in the numerator and the denominator. $\newline$ Numerator: $a(5a^2-125)$ $\newline$ Denominator: $5a(a+5)$
Factor Out Common Terms: Factor out common terms in the numerator. $\newline$ $a(5a^2-125) = a(5(a^2-25))$
Factor Difference of Squares: Recognize that $a^2-25$ is a difference of squares and can be factored further. $\newline$ $5(a^2-25) = 5(a+5)(a-5)$
Rewrite Numerator: Rewrite the numerator with its factored form. $a(5(a+5)(a-5))$
Cancel Common Terms: Cancel out the common terms in the numerator and the denominator. $\newline$ The common term is $5a(a+5)$ . $\newline$ So, $\frac{a(5(a+5)(a-5))}{5a(a+5)} = (a-5)$

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