Solve 1/4-9a^2

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

Factor

$$\frac{\left(-6a-1\right)\left(6a-1\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{1-36a^{2}}{4}$$

Consider 1-36a^{2}. Rewrite 1-36a^{2} as 1^{2}-\left(6a\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(1-6a\right)\left(1+6a\right)$$

Reorder the terms.

$$\left(-6a+1\right)\left(6a+1\right)$$

Rewrite the complete factored expression.

$$\frac{\left(-6a+1\right)\left(6a+1\right)}{4}$$

Evaluate

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