Solve x^3y^2-343y^5

$${ x }^{ 3 } { y }^{ 2 } -343 { y }^{ 5 }$$

Factor

$$\left(x-7y\right)y^{2}\left(x^{2}+7xy+49y^{2}\right)$$

Solution Steps

Factor out y^{2}.

$$y^{2}\left(x^{3}-343y^{3}\right)$$

Consider x^{3}-343y^{3}. Rewrite x^{3}-343y^{3} as x^{3}-\left(7y\right)^{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).

$$\left(x-7y\right)\left(x^{2}+7xy+49y^{2}\right)$$

Rewrite the complete factored expression.

$$y^{2}\left(x-7y\right)\left(x^{2}+7xy+49y^{2}\right)$$

Evaluate

$$y^{2}\left(x^{3}-343y^{3}\right)$$