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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$- 4 m ^ { 2 } + 35 ^ { 2 } n ^ { 2 }$$

Factor

$\left(-2m-35n\right)\left(2m-35n\right)$

Solution Steps

Multiply and combine like terms.

$$-4m^{2}+1225n^{2}$$

Rewrite $-4m^{2}+1225n^{2}$ as $\left(35n\right)^{2}-\left(2m\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(35n-2m\right)\left(35n+2m\right)$$

Reorder the terms.

$$\left(-2m+35n\right)\left(2m+35n\right)$$

Evaluate

$1225n^{2}-4m^{2}$