Solve 4/9a^2-1/16b^2

$$\frac { 4 } { 9 } a ^ { 2 } - \frac { 1 } { 16 } b ^ { 2 }$$

Factor

$$\frac{\left(8a-3b\right)\left(8a+3b\right)}{144}$$

Solution Steps

Factor out \frac{1}{144}.

$$\frac{64a^{2}-9b^{2}}{144}$$

Consider 64a^{2}-9b^{2}. Rewrite 64a^{2}-9b^{2} as \left(8a\right)^{2}-\left(3b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(8a-3b\right)\left(8a+3b\right)$$

Rewrite the complete factored expression.

$$\frac{\left(8a-3b\right)\left(8a+3b\right)}{144}$$

Evaluate

$$\frac{4a^{2}}{9}-\frac{b^{2}}{16}$$