Solve x^3y-x^3y-x^5+x^3

$$x ^ { 3 } y - x ^ { 3 } y - x ^ { 5 } + x ^ { 3 }$$

Evaluate

$$x^{3}-x^{5}$$

Solution Steps

Combine x^{3}y and -x^{3}y to get 0.

$$0-x^{5}+x^{3}$$

Anything plus zero gives itself.

$$-x^{5}+x^{3}$$

Factor

$$\left(-x-1\right)\left(x-1\right)x^{3}$$

Solution Steps

Factor out x^{3}.

$$x^{3}\left(y-y-x^{2}+1\right)$$

Consider y-y-x^{2}+1. Multiply and combine like terms.

$$-x^{2}+1$$

Consider -x^{2}+1. Rewrite -x^{2}+1 as 1^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-x\right)\left(1+x\right)$$

Reorder the terms.

$$\left(-x+1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$x^{3}\left(-x+1\right)\left(x+1\right)$$