Solve ax^4-ay^4

$$a x ^ { 4 } - a y ^ { 4 }$$

Factor

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

Solution Steps

Factor out a.

$$a\left(x^{4}-y^{4}\right)$$

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

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

Consider x^{2}-y^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Rewrite the complete factored expression.

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

Evaluate

$$a\left(x^{4}-y^{4}\right)$$