Solve 9m ^ 2 - 1/4 * n ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$9m^{2}-\frac{1}{4}n^{2}$$

Factor

$\frac{\left(6m-n\right)\left(6m+n\right)}{4}$

Solution Steps

Factor out $\frac{1}{4}$.

$$\frac{36m^{2}-n^{2}}{4}$$

Consider $36m^{2}-n^{2}$. Rewrite $36m^{2}-n^{2}$ as $\left(6m\right)^{2}-n^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(6m-n\right)\left(6m+n\right)$$

Rewrite the complete factored expression.

$$\frac{\left(6m-n\right)\left(6m+n\right)}{4}$$

Evaluate

$-\frac{n^{2}}{4}+9m^{2}$