Solve ax^3-by^3+bx^3-ay^3

$$a x ^ { 3 } - b y ^ { 3 } + b x ^ { 3 } - a y ^ { 3 }$$

Factor

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

Solution Steps

Do the grouping ax^{3}-by^{3}+bx^{3}-ay^{3}=\left(ax^{3}-ay^{3}\right)+\left(bx^{3}-by^{3}\right), and factor out a in the first and b in the second group.

$$a\left(x^{3}-y^{3}\right)+b\left(x^{3}-y^{3}\right)$$

Factor out common term x^{3}-y^{3} by using distributive property.

$$\left(x^{3}-y^{3}\right)\left(a+b\right)$$

Consider x^{3}-y^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

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

Rewrite the complete factored expression.

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

Evaluate

$$\left(a+b\right)\left(x^{3}-y^{3}\right)$$