QuestionJuly 16, 2025

Find the quotient. (-6m^2+96n^2)/(3m+12n)

Find the quotient. (-6m^2+96n^2)/(3m+12n)
Find the quotient. (-6m^2+96n^2)/(3m+12n)

Solution
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Answer

-2(m - 4n) Explanation 1. Factor the numerator Factor out the greatest common factor from -6m^2 + 96n^2. The GCF is 6, so we have -6(m^2 - 16n^2). 2. Recognize a difference of squares Notice that m^2 - 16n^2 is a difference of squares: (m - 4n)(m + 4n). 3. Simplify the expression Substitute back into the original fraction: \frac{-6(m - 4n)(m + 4n)}{3m + 12n}. 4. Factor the denominator Factor 3m + 12n as 3(m + 4n). 5. Cancel common factors Cancel the common factor (m + 4n) from the numerator and denominator.

Explanation

1. Factor the numerator<br /> Factor out the greatest common factor from $-6m^2 + 96n^2$. The GCF is $6$, so we have $-6(m^2 - 16n^2)$.<br /><br />2. Recognize a difference of squares<br /> Notice that $m^2 - 16n^2$ is a difference of squares: $(m - 4n)(m + 4n)$.<br /><br />3. Simplify the expression<br /> Substitute back into the original fraction: $\frac{-6(m - 4n)(m + 4n)}{3m + 12n}$.<br /><br />4. Factor the denominator<br /> Factor $3m + 12n$ as $3(m + 4n)$.<br /><br />5. Cancel common factors<br /> Cancel the common factor $(m + 4n)$ from the numerator and denominator.
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