Solve 3x^4+375xy^3

$$3 x ^ { 4 } + 375 x y ^ { 3 }$$

Factor

$$3x\left(x+5y\right)\left(x^{2}-5xy+25y^{2}\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{4}+125xy^{3}\right)$$

Consider x^{4}+125xy^{3}. Factor out x.

$$x\left(x^{3}+125y^{3}\right)$$

Consider x^{3}+125y^{3}. Rewrite x^{3}+125y^{3} as x^{3}+\left(5y\right)^{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).

$$\left(x+5y\right)\left(x^{2}-5xy+25y^{2}\right)$$

Rewrite the complete factored expression.

$$3x\left(x+5y\right)\left(x^{2}-5xy+25y^{2}\right)$$

Evaluate

$$3x\left(x^{3}+125y^{3}\right)$$