Solve 4q^4-16r^2

$$4 q ^ { 4 } - 16 r ^ { 2 }$$

Factor

$$4\left(q^{2}-2r\right)\left(q^{2}+2r\right)$$

Solution Steps

Factor out 4.

$$4\left(q^{4}-4r^{2}\right)$$

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

$$\left(q^{2}-2r\right)\left(q^{2}+2r\right)$$

Rewrite the complete factored expression.

$$4\left(q^{2}-2r\right)\left(q^{2}+2r\right)$$

Evaluate

$$4\left(q^{4}-4r^{2}\right)$$