Question

Explain how you identify the like terms in the expression$8a^2+4a+9-a^2-1$.

Short answer

If the terms contain the same variables and same exponent or the terms are constants then they are called like terms. Here, $8a^2$and $a^2$are like terms, $9$ and 1 are like terms. There are like terms for the term 4a.

Step-by-step solution

Step 1. Given Information

The given expression is $8a^2+4a+9-a^2-1$.

Step 2.  Identify the terms in the given expression.

• In the algebraic expression, the term can be a constant or a product of a constant and one or more variables.
• In the given expression, there are 5 terms that are $8a^2$, $a^2$, 4a, 9, and 1.

Step 3. Identify the like terms. 

• If the terms contain the same variables and same exponent or the terms are constants then they are called like terms.
• It is observed that the terms $8a^2$, $a^2$are like terms since they are having the same variable and same exponent.
• The constants 9 and 1 are like terms since they are constants.
• There are no like terms for the term 4a.

Step 3. Conclusion.

The terms $8a^2$,$a^2$are like terms and 9 and 1 are like terms.