An expression is shown below:2x3y + 8xy − 4x2y − 16yPart A: Rewrite the expression by factoring out the greatest common factor. (4 points)Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Part A: Rewrite the expression by factoring out the greatest common factor.

Given expression: $2x^3y + 8xy - 4x^2y - 16y$

Step 1: Identify the greatest common factor (GCF) of all the terms.

• The GCF of the coefficients (2, 8, -4, -16) is 2.
• The GCF of the variable parts (considering $x$ and $y$) is $y$.

Step 2: Factor out the GCF from each term.

• The GCF of the entire expression is $2y$.

So, the expression can be rewritten as: $2y(x^3 + 4x - 2x^2 - 8)$

Part B: Factor the entire expression completely.

Step 1: Simplify the expression inside the parentheses. $2y(x^3 + 4x - 2x^2 - 8)$

Step 2: Rearrange the terms inside the parentheses to make it easier to factor by grouping. $2y(x^3 - 2x^2 + 4x - 8)$

Step 3: Factor by grouping. Group the terms in pairs: $2y[(x^3 - 2x^2) + (4x - 8)]$

Step 4: Factor out the common factors from each group. $2y[x^2(x - 2) + 4(x - 2)]$

Step 5: Notice that $(x - 2)$ is a common factor in both groups. $2y[(x - 2)(x^2 + 4)]$

So, the completely factored expression is: $2y(x - 2)(x^2 + 4)$