Solve 2x^2-32x^4

$$2 x ^ { 2 } - 32 x ^ { 4 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{2}-16x^{4}\right)$$

Consider x^{2}-16x^{4}. Factor out x^{2}.

$$x^{2}\left(1-16x^{2}\right)$$

Consider 1-16x^{2}. Rewrite 1-16x^{2} as 1^{2}-\left(4x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-4x\right)\left(1+4x\right)$$

Reorder the terms.

$$\left(-4x+1\right)\left(4x+1\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$2x^{2}-32x^{4}$$