Solve x^4y^3-1000x

$$x ^ { 4 } y ^ { 3 } - 1000 x$$

Factor

$$x\left(xy-10\right)\left(x^{2}y^{2}+10xy+100\right)$$

Solution Steps

Factor out x.

$$x\left(x^{3}y^{3}-1000\right)$$

Consider x^{3}y^{3}-1000. Rewrite x^{3}y^{3}-1000 as \left(xy\right)^{3}-10^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(xy-10\right)\left(x^{2}y^{2}+10xy+100\right)$$

Rewrite the complete factored expression.

$$x\left(xy-10\right)\left(x^{2}y^{2}+10xy+100\right)$$

Evaluate

$$x\left(\left(xy\right)^{3}-1000\right)$$