Solve 243x^4-3t^4

$$243 x ^ { 4 } - 3 t ^ { 4 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(81x^{4}-t^{4}\right)$$

Consider 81x^{4}-t^{4}. Rewrite 81x^{4}-t^{4} as \left(9x^{2}\right)^{2}-\left(t^{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).

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

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

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

Rewrite the complete factored expression.

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

Evaluate

$$243x^{4}-3t^{4}$$