Solve 24y^4-6y^2

$$24 y ^ { 4 } - 6 y ^ { 2 }$$

Factor

$$6\left(2y-1\right)\left(2y+1\right)y^{2}$$

Solution Steps

Factor out 6.

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

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

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

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

$$\left(2y-1\right)\left(2y+1\right)$$

Rewrite the complete factored expression.

$$6y^{2}\left(2y-1\right)\left(2y+1\right)$$

Evaluate

$$24y^{4}-6y^{2}$$