Solve 81x^4-256y^4

$$81 x ^ { 4 } - 256 y ^ { 4 }$$

Factor

$$\left(3x-4y\right)\left(3x+4y\right)\left(9x^{2}+16y^{2}\right)$$

Solution Steps

Rewrite 81x^{4}-256y^{4} as \left(9x^{2}\right)^{2}-\left(16y^{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).

$$\left(9x^{2}-16y^{2}\right)\left(9x^{2}+16y^{2}\right)$$

Consider 9x^{2}-16y^{2}. Rewrite 9x^{2}-16y^{2} as \left(3x\right)^{2}-\left(4y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-4y\right)\left(3x+4y\right)$$

Rewrite the complete factored expression.

$$\left(3x-4y\right)\left(3x+4y\right)\left(9x^{2}+16y^{2}\right)$$

Evaluate

$$81x^{4}-256y^{4}$$