Question

for each expression, select all equivalent expressions from the list.
(a) ( 10x - 4x + 7x )
( square 6x + 7x )
( square 13 + x )
( square 7x - 6x )
( square 13x )
(b) ( 4(1 + 2y) )
( square 4 + 1 cdot 4 + 2y )
( square 4 + 8y )
( square 4 cdot 1 + 4 cdot 2y )
( square 4 + 2y )

Explanation:

Step1: Simplify part (a) expression

First, simplify \(10x - 4x + 7x\). Combine like terms: \(10x-4x = 6x\), then \(6x + 7x=13x\). Also, check other options:

• \(6x + 7x\): Combine like terms, \(6x+7x = 13x\), same as simplified (a).
• \(7x - 6x\): \(7x-6x=x\), not equal to \(13x\).
• \(13 + x\): This is a constant and a variable term, not equal to \(13x\).
• \(13x\): Already the simplified form, equal.

Step2: Simplify part (b) expression

Simplify \(4(1 + 2y)\) using distributive property: \(4\times1+4\times2y = 4 + 8y\)? Wait, no, wait: \(4(1 + 2y)=4\times1+4\times2y = 4 + 8y\)? Wait, no, wait the options: Wait, let's re - check. Wait, \(4(1 + 2y)=4\times1+4\times2y=4 + 8y\)? Wait, no, the options: Let's see the options for (b):

• \(4 + 1\cdot4+2y\): \(4 + 4+2y=8 + 2y\), no.
• \(4\cdot1+4\cdot2y\): By distributive property, \(4(1 + 2y)=4\times1+4\times2y\), which is equal.
• \(4 + 8y\): Since \(4\times2y = 8y\), so \(4(1 + 2y)=4 + 8y\), equal.
• \(4 + 2y\): No, missing the \(8y\) part.

Answer:

For part (a): The equivalent expressions are \(6x + 7x\) and \(13x\).
For part (b): The equivalent expressions are \(4\cdot1 + 4\cdot2y\) and \(4 + 8y\).