Solve 64x^4y^2-27xy^5

$$64 { x }^{ 4 } { y }^{ 2 } -27x { y }^{ 5 }$$

Factor

$$x\left(4x-3y\right)y^{2}\left(16x^{2}+12xy+9y^{2}\right)$$

Solution Steps

Factor out xy^{2}.

$$xy^{2}\left(64x^{3}-27y^{3}\right)$$

Consider 64x^{3}-27y^{3}. Rewrite 64x^{3}-27y^{3} as \left(4x\right)^{3}-\left(3y\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).

$$\left(4x-3y\right)\left(16x^{2}+12xy+9y^{2}\right)$$

Rewrite the complete factored expression.

$$xy^{2}\left(4x-3y\right)\left(16x^{2}+12xy+9y^{2}\right)$$

Evaluate

$$xy^{2}\left(64x^{3}-27y^{3}\right)$$