Solve 100x^4-400x^2

$$100 x ^ { 4 } - 400 x ^ { 2 }$$

Factor

$$100\left(x-2\right)\left(x+2\right)x^{2}$$

Solution Steps

Factor out 100.

$$100\left(x^{4}-4x^{2}\right)$$

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

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

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

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$100x^{2}\left(x-2\right)\left(x+2\right)$$

Evaluate

$$100x^{2}\left(x^{2}-4\right)$$