Solve 3x^7y-81x^4y^4

$$3 x ^ { 7 } y - 81 x ^ { 4 } y ^ { 4 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{7}y-27x^{4}y^{4}\right)$$

Consider x^{7}y-27x^{4}y^{4}. Factor out x^{4}y.

$$x^{4}y\left(x^{3}-27y^{3}\right)$$

Consider x^{3}-27y^{3}. Rewrite x^{3}-27y^{3} as x^{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).

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

Rewrite the complete factored expression.

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

Evaluate

$$3yx^{7}-81\left(xy\right)^{4}$$