Which expression is equivalent to w + 8w + 2

Which expression is equivalent to w + 8w + 2

The correct answer and explanation is:

The correct expression equivalent to w+8w+2w + 8w + 2 is 9w+29w + 2.

Here’s how to simplify it:

1. Identify like terms:
   In the expression w+8w+2w + 8w + 2, the terms involving ww are ww and 8w8w. These are like terms because both contain the variable ww.
2. Combine the like terms:
   The term ww can be thought of as 1w1w, so when you add 1w1w and 8w8w, you get: 1w+8w=9w1w + 8w = 9w
3. Include the constant term:
   The term 22 is a constant and cannot be combined with any other terms that contain variables. So, after simplifying the variable terms, the expression becomes: 9w+29w + 2
4. Final expression:
   The simplified version of w+8w+2w + 8w + 2 is therefore 9w+29w + 2, which is the expression where the like terms are combined, and the constant term is left as is.

This process of simplifying an algebraic expression involves recognizing like terms (terms that have the same variable) and combining their coefficients. Any constants, such as the 2 in this case, are kept separate as they are not like terms with the variable parts.