Solve 3a^2b^2-12a^4

$$3 a ^ { 2 } b ^ { 2 } - 12 a ^ { 4 }$$

Factor

$$3\left(b-2a\right)\left(2a+b\right)a^{2}$$

Solution Steps

Factor out 3.

$$3\left(a^{2}b^{2}-4a^{4}\right)$$

Consider a^{2}b^{2}-4a^{4}. Factor out a^{2}.

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

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.

$$3a^{2}\left(-2a+b\right)\left(2a+b\right)$$

Evaluate

$$3\left(ab\right)^{2}-12a^{4}$$