Solve 3y^2-12y^6

$$3 { y }^{ 2 } -12 { y }^{ 6 }$$

Factor

$$3y^{2}\left(-2y^{2}-1\right)\left(2y^{2}-1\right)$$

Solution Steps

Factor out 3.

$$3\left(y^{2}-4y^{6}\right)$$

Consider y^{2}-4y^{6}. Factor out y^{2}.

$$y^{2}\left(1-4y^{4}\right)$$

Consider 1-4y^{4}. Rewrite 1-4y^{4} as 1^{2}-\left(2y^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-2y^{2}\right)\left(1+2y^{2}\right)$$

Reorder the terms.

$$\left(-2y^{2}+1\right)\left(2y^{2}+1\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -2y^{2}+1,2y^{2}+1.

$$3y^{2}\left(-2y^{2}+1\right)\left(2y^{2}+1\right)$$

Evaluate

$$3y^{2}-12y^{6}$$