Solve 1/4a^2-4s^2

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

Factor

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

Solution Steps

Factor out \frac{1}{4}.

$$\frac{a^{2}-16s^{2}}{4}$$

Consider a^{2}-16s^{2}. Rewrite a^{2}-16s^{2} as a^{2}-\left(4s\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(a-4s\right)\left(a+4s\right)$$

Reorder the terms.

$$\left(-4s+a\right)\left(4s+a\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$\frac{a^{2}}{4}-4s^{2}$$