Question

Identify the pair of equivalent expressions.(1 point) Responses 2x+2 %C2%A0and%C2%A02(x+2) %C2%A0 2 x plus 2%C2%A0and%C2%A02 times open paren x plus 2 close paren 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 2(x+3) %C2%A0and%C2%A02x+6 2 times open paren x plus 3 close paren%C2%A0and%C2%A02 x plus 6 −3(x+2) %C2%A0and%C2%A0−3x−3

Answer 1

To identify the pair of equivalent expressions, let's simplify each option:

1. \(2x + 2\) and \(2(x + 2)\):

   • \(2(x + 2) = 2x + 4\)
   • These expressions are not equivalent.

2. \(3x + 2x\) and \(x^2(3 + 2)\):

   • \(3x + 2x = 5x\)
   • \(x^2(3 + 2) = x^2 \cdot 5 = 5x^2\)
   • These expressions are not equivalent.

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

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

4. \(-3(x + 2)\) and \(-3x - 3\):

   • \(-3(x + 2) = -3x - 6\)
   • These expressions are not equivalent.

The only pair of equivalent expressions is \(2(x + 3)\) and \(2x + 6\).