Solve 100z^2-4z^4

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

Factor

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

Solution Steps

Factor out 4.

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

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

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

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

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

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