Question

An expression is shown below:

Answer 1

Answer:

(a)$3y(x^3+4x-3x^2-12)$

(b)$3y(x^2+4)(x-3)$

Step-by-step explanation:

Given the expression: $3x^3y + 12xy - 9x^2y -36y$

Part A

If we consider the terms: $3x^3y ,12xy,9x^2y,36y$ in the expression. The common terms are 3 and y.

Therefore the greatest common factor of the terms is 3y.

Factoring this out, we obtain:

$3x^3y + 12xy - 9x^2y -36y=3y(x^3+4x-3x^2-12)$

Part B

Next, we factor the expression completely

$3x^3y + 12xy - 9x^2y -36y\\=3y(x^3+4x-3x^2-12)\\ Rearranging we obtain:\\=3y(x^3-3x^2+4x-12)\\=3y[x^2(x-3)+4(x-3)]\\=3y(x^2+4)(x-3)$