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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$( 84 x ^ { 2 } - 21 )$$

Factor

$21\left(2x-1\right)\left(2x+1\right)$

Solution Steps

Factor out $21$.

$$21\left(4x^{2}-1\right)$$

Consider $4x^{2}-1$. Rewrite $4x^{2}-1$ as $\left(2x\right)^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(2x-1\right)\left(2x+1\right)$$

Rewrite the complete factored expression.

$$21\left(2x-1\right)\left(2x+1\right)$$

Evaluate

$84x^{2}-21$