Solve 100y^2-4y^4

$$100 y ^ { 2 } - 4 y ^ { 4 }$$

Factor

$$4\left(-y-5\right)\left(y-5\right)y^{2}$$

Solution Steps

Factor out 4.

$$4\left(25y^{2}-y^{4}\right)$$

Consider 25y^{2}-y^{4}. Factor out y^{2}.

$$y^{2}\left(25-y^{2}\right)$$

Consider 25-y^{2}. Rewrite 25-y^{2} as 5^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5-y\right)\left(5+y\right)$$

Reorder the terms.

$$\left(-y+5\right)\left(y+5\right)$$

Rewrite the complete factored expression.

$$4y^{2}\left(-y+5\right)\left(y+5\right)$$

Evaluate

$$100y^{2}-4y^{4}$$