Solve 12a-12ab^2+3ab^4=

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

Factor

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

Solution Steps

Factor out 3.

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

Consider 4a-4ab^{2}+ab^{4}. Factor out a.

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

Consider 4-4b^{2}+b^{4}. Use the perfect square formula, p^{2}-2pq+q^{2}=\left(p-q\right)^{2}, where p=b^{2} and q=2.

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

Rewrite the complete factored expression. Polynomial b^{2}-2 is not factored since it does not have any rational roots.

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

Evaluate

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