Question

sharina simplified the expression \\(3(2x - 6 - x + 1)^2 - 2 + 4x\\). in step 1 she simplified within the parentheses. in step 2 she expanded the exponent.

sharinas work

\\3(2x - 6 - x + 1)^2 - 2 + 4x\\

step 1: \\3(x - 5)^2 - 2 + 4x\\
step 2: \\3(x^2 - 10x + 25) - 2 + 4x\\
step 3:
step 4:

which is a possible next step?

• simplify the expression by adding and subtracting from left to right.
• combine like terms within the parentheses.
• combine all x-terms.
• distribute the 3 to each term in the parentheses by multiplying.

Explanation:

Analyze the current step in the work

The expression in Step 2 of Sharina's work is:

$$3(x^2 - 10x + 25) - 2 + 4x$$

This expression consists of a constant \(3\) multiplied by a trinomial in parentheses, followed by subtraction and addition terms.

Determine the next logical operation

Using Polynomial Operations, we follow the standard order of operations (PEMDAS/GEMS). Since the exponent has already been expanded, the next step is to address the multiplication. We must multiply the factor \(3\) by each term inside the parentheses.

Identify the mathematical property to apply

Using the Distributive Property, we distribute the coefficient \(3\) to each term inside the trinomial:

$$3 \cdot x^2 + 3 \cdot (-10x) + 3 \cdot 25$$

This matches the option: "Distribute the 3 to each term in the parentheses by multiplying."

Answer:

• Simplify the expression by adding and subtracting from left to right.
• Combine like terms within the parentheses.
• Combine all x-terms.
• Distribute the 3 to each term in the parentheses by multiplying. (Correct answer)