Solve 81x^4y+3xy^4

$$81 x ^ { 4 } y + 3 x y ^ { 4 }$$

Factor

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

Solution Steps

Factor out 3.

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

Consider 27x^{4}y+xy^{4}. Factor out xy.

$$xy\left(27x^{3}+y^{3}\right)$$

Consider 27x^{3}+y^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

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

Rewrite the complete factored expression.

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

Evaluate

$$3xy\left(27x^{3}+y^{3}\right)$$