Question

Factor completely:
5x2y3 – 180y
​

Answer 1

`\large\boxed{5x^2y^3-180y=(5y)(xy-6)(xy+6)}`

Explanation:

`5x^2y^3=(5y)(x^2y^2)\\\\180y=(5y)(36)\\\\5x^2y^3-180y=(5y)(x^2y^2)-(5y)(36)=(5y)(x^2y^2-36)\\\\\text{use}\ (ab)^n=a^nb^n\\\\=(5y)\bigg((xy)^2-6^2\bigg)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\(5y)(xy-6)(xy+6)`