Question

Factor the expression completely.

$12x^2{y}^4-3x{y}^5+9x^3{y}^2$

Short answer

Factorized form of$12x^2{y}^4-3x{y}^5+9x^3{y}^2$is $\left(3x{y}^2\right)\left(4x{y}^2-y^3+3x^2\right)$.

Step-by-step solution

Step 1. Take the common out of the expression.

$12x^2{y}^4-3x{y}^5+9x^3{y}^2=3x{y}^2\left(4x{y}^2-y^3+3x^2\right)$

Step 2. Re write the expression after factorizing the expression.

$12x^2{y}^4-3x{y}^5+9x^3{y}^2=3x{y}^2\left(4x{y}^2-y^3+3x^2\right)$

Here we may observe that there is no further possible factorization of the given expression.

Step 3. Factorized from of the expression is:

$12x^2{y}^4-3x{y}^5+9x^3{y}^2=\left(3x{y}^2\right)\left(4x{y}^2-y^3+3x^2\right)$