Factor the Expression: 256xy³-32zy² Step-by-Step

To solve this problem, we'll follow these steps to factor $256xy^3 - 32zy^2$:

• Step 1: Identify the greatest common factor (GCF) for both terms.
• Step 2: Factor out the GCF from the expression.

Now, let's work through each step:

Step 1: Identify the GCF.
The first term is $256xy^3$, and the second term is $32zy^2$.

• The numerical GCF of 256 and 32 is 32.
• The terms $xy^3$ and $zy^2$ have a common factor of $y^2$.

Thus, the GCF of the entire expression is $32y^2$.

Step 2: Factor out the GCF.
We'll factor $32y^2$ out of each term:

• The first term $256xy^3$ becomes $32y^2 \times 8xy$. (since $\frac{256xy^3}{32y^2} = 8xy$)
• The second term $32zy^2$ becomes $32y^2 \times z$. (since $\frac{32zy^2}{32y^2} = z$)

Therefore, factoring the expression by the GCF gives us:
$256xy^3 - 32zy^2 = 32y^2(8xy - z)$.

The factorized form of the expression is $32y^2(8xy - z)$.