Solve 1-81x^4

$$1-81 { x }^{ 4 }$$

Factor

$$\left(3x-1\right)\left(3x+1\right)\left(-9x^{2}-1\right)$$

Solution Steps

Rewrite 1-81x^{4} as 1^{2}-\left(9x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-9x^{2}\right)\left(1+9x^{2}\right)$$

Reorder the terms.

$$\left(-9x^{2}+1\right)\left(9x^{2}+1\right)$$

Consider -9x^{2}+1. Rewrite -9x^{2}+1 as 1^{2}-\left(3x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-3x\right)\left(1+3x\right)$$

Reorder the terms.

$$\left(-3x+1\right)\left(3x+1\right)$$

Rewrite the complete factored expression. Polynomial 9x^{2}+1 is not factored since it does not have any rational roots.

$$\left(-3x+1\right)\left(3x+1\right)\left(9x^{2}+1\right)$$

Evaluate

$$1-81x^{4}$$