Solve 2ax^3-bx^3-2ay^3+by^3

$$2 a x ^ { 3 } - b x ^ { 3 } - 2 a y ^ { 3 } + b y ^ { 3 }$$

Factor

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

Solution Steps

Do the grouping 2ax^{3}-bx^{3}-2ay^{3}+by^{3}=\left(2ax^{3}-bx^{3}\right)+\left(-2ay^{3}+by^{3}\right), and factor out x^{3} in the first and -y^{3} in the second group.

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

Factor out common term 2a-b by using distributive property.

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

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.

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

Evaluate

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