Solve 3-27x^4y^4

$$3-27 { x }^{ 4 } { y }^{ 4 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(1-9x^{4}y^{4}\right)$$

Consider 1-9x^{4}y^{4}. Rewrite 1-9x^{4}y^{4} as 1^{2}-\left(3x^{2}y^{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).

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

$$3-27\left(xy\right)^{4}$$