Solve 3x^4y-1875y^5

$$3 x ^ { 4 } y - 1875 y ^ { 5 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{4}y-625y^{5}\right)$$

Consider x^{4}y-625y^{5}. Factor out y.

$$y\left(x^{4}-625y^{4}\right)$$

Consider x^{4}-625y^{4}. Rewrite x^{4}-625y^{4} as \left(x^{2}\right)^{2}-\left(25y^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Consider x^{2}-25y^{2}. Rewrite x^{2}-25y^{2} as x^{2}-\left(5y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5y\right)\left(x+5y\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$3y\left(x^{4}-625y^{4}\right)$$