Solve 8a^2b^2-2b^2

$$8 a ^ { 2 } b ^ { 2 } - 2 b ^ { 2 }$$

Factor

$$2\left(2a-1\right)\left(2a+1\right)b^{2}$$

Solution Steps

Factor out 2.

$$2\left(4a^{2}b^{2}-b^{2}\right)$$

Consider 4a^{2}b^{2}-b^{2}. Factor out b^{2}.

$$b^{2}\left(4a^{2}-1\right)$$

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

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

Rewrite the complete factored expression.

$$2b^{2}\left(2a-1\right)\left(2a+1\right)$$

Evaluate

$$8\left(ab\right)^{2}-2b^{2}$$