Solve 4b^2-16a^2

$$4 b ^ { 2 } - 16 a ^ { 2 }$$

Factor

$$4\left(b-2a\right)\left(2a+b\right)$$

Solution Steps

Factor out 4.

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

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

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

Reorder the terms.

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

Rewrite the complete factored expression.

$$4\left(-2a+b\right)\left(2a+b\right)$$

Evaluate

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