Question: For each expression, select all equivalent expressions from the list. (a) \(4(7x - 6)\) - \(28x…

For each expression, select all equivalent expressions from the list.

(a) \(4(7x - 6)\)

• \(28x - 6\)
• \(28x - 24\)
• \(11x - 6\)
• \(4 \cdot 7x - 4 \cdot 6\)

(b) \(12y + 3y + 2y\)

• \(17y\)
• \(12y - 5y\)
• \(12y + 5y\)
• \(17 + y\)

Solution

For each expression, we need to identify all equivalent expressions from the list provided. ### (a) \(4(7x - 6)\) First, distribute the 4 in the expression: \[ 4(7x - 6) = 4 \cdot 7x - 4 \cdot 6 \] Simplify the terms: \[ = 28x - 24 \] Thus, the equivalent expressions for (a) are: \(28x - 24\). ### (b) \(12y + 3y + 2y\) Combine like terms: \[ = (12y + 3y + 2y) = 17y \] Thus, the equivalent expression for (b) is: \(17y\).