Question

Identify the pair of equivalent expressions.(1 point) Responses 3x+2x %C2%A0and%C2%A0x2(3+2) %C2%A0 3 x plus 2 x%C2%A0and%C2%A0x squared times open paren 3 plus 2 close paren 3x+2 %C2%A0and%C2%A03(x+2) %C2%A0 3 x plus 2%C2%A0and%C2%A03 times open paren x plus 2 close paren 3(x+2) %C2%A0and%C2%A03x+6 3 times open paren x plus 2 close paren%C2%A0and%C2%A03 x plus 6 −3(x+2) %C2%A0and%C2%A0−6x−3 %C2%A0 negative 3 times open paren x plus 2 close paren%C2%A0and%C2%A0negative 6 x minus 3

Answer 1

To identify the pair of equivalent expressions, let’s simplify each expression provided in the options:

1. **Option 1:**
- \(3x + 2x\) simplifies to \(5x\).
- \(x^2(3 + 2)\) simplifies to \(5x^2\).

These are not equivalent since \(5x \neq 5x^2\).

2. **Option 2:**
- \(3x + 2\) remains \(3x + 2\).
- \(3(x + 2)\) expands to \(3x + 6\).

These are not equivalent since \(3x + 2 \neq 3x + 6\).

3. **Option 3:**
- \(3(x + 2)\) expands to \(3x + 6\).
- \(3x + 6\) also stands as \(3x + 6\).

These are equivalent since \(3(x + 2) = 3x + 6\).

4. **Option 4:**
- \(-3(x + 2)\) expands to \(-3x - 6\).
- \(-6x - 3\) is not equivalent to \(-3x - 6\).

These are not equivalent since \(-3x - 6 \neq -6x - 3\).

From the analysis above, the pair of equivalent expressions is:

**Option 3:** \(3(x + 2)\) and \(3x + 6\).