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

\\(\

$$\begin{array}{|c|c|} \\hline & 3(2x - 6 - x - 1)^2 - 2 + 4x \\\\ \\hline 1 & 3(x - 5)^2 - 2 + 4x \\\\ \\hline 2 & 3(x^2 - 10x + 25) - 2 + 4x \\\\ \\hline 3 & \\\\ \\hline 4 & \\\\ \\hline \\end{array}$$

\\)

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 expression at Step 2

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

Evaluate the proposed next steps

• "Simplify the expression by adding and subtracting from left to right": Incorrect, order of operations requires multiplication (distribution) before addition/subtraction.
• "Combine like terms within the parentheses": Incorrect, \(x^2\), \(-10x\), and \(25\) are not like terms.
• "Combine all x-terms": Incorrect, the \(x\)-term inside the parentheses is multiplied by \(3\) and cannot be combined with \(4x\) yet.
• "Distribute the 3 to each term in the parentheses by multiplying": Correct, according to the order of operations, distribution of the coefficient \(3\) must occur before combining terms outside.

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)