Questions: Write this expression in its most simplified, factored form. 12x^2y - 32xy + 8y

Transcript text: Write this expression in its most simplified, factored form. \[ 12 x^{2} y-32 x y+8 y \] Do not include multiplication symbols ( $\cdot$ or $x$ ) between factors

Solution

Solution Steps

To factor the polynomial $12x^2y - 32xy + 8y$, we first look for the greatest common factor (GCF) of all the terms. The GCF in this case is $4y$. We then factor out $4y$ from each term and simplify the resulting expression.

Step 1: Identify the Greatest Common Factor (GCF)

To factor the polynomial $12x^2y - 32xy + 8y$, we first identify the greatest common factor (GCF) of all the terms. The GCF in this case is $4y$.

Step 2: Factor Out the GCF

Next, we factor out $4y$ from each term in the polynomial: \[ 12x^2y - 32xy + 8y = 4y(3x^2 - 8x + 2) \]