1. Do Now
Evaluate each algebraic expression for y = 3.
3y + y y
3. 10y – 4y y2 + y - 2 12 21 18 46

2. Goal:
Learn to identify like terms and simplify algebraic expressions.

3. In the algebraic expression 5y2 + y - 2, 5y2, y, and 2 are called terms. A term can be a number (constant), a variable, or a product of numbers and variables. Terms in an expression are separated by + and –.
5y y
term
term
term

4. In the term 7x, 7 is called the coefficient
In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression.
A variable by itself, like y, has a coefficient of 1. So y = 1y.
Coefficient
Variable 7 x

5. Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants are also like terms.
Like Terms
Unlike Terms
3x and 2x
w2 and
3w2
5 and 1.8
5x2 and 2x
6a and 6b
3.2 and n
Only one term
contains a
variable
The exponents
are different.
The variables
are different

6. Example A
Identify like terms in the list.
3t 5w2 7t 9v w2 8v
Look for like variables with like powers.
3t 5w2 7t 9v w2 8v
Like terms: 3t and 7t 5w2 and 4w2 9v and 8v
Use different shapes or colors to indicate sets of like terms.
Helpful Hint

7. Identify like terms in the list.
2x 4y3 8x 5z y3 8z
Look for like variables with like powers.
2x 4y3 8x 5z y3 8z
Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

8. + = Combining like terms is like grouping similar objects. x x x x x x
To combine like terms that have variables, add or
subtract the coefficients.

9. Example B
Simplify the algebraic expressions.
6t – 4t
6t – 4t
6t and 4t are like terms. 2t
Subtract the coefficients.
45x – 37y + 87
In this expression, there are no like terms
to combine.

10. Example B
Simplify the algebraic expressions.
3a2 + 5b + 11b2 – 4b + 2a2 – 6
Identify like
terms.
3a2 + 5b + 11b2 – 4b + 2a2 – 6
Group like
terms.
(3a2 + 2a2) + (5b – 4b) + 11b2 – 6
5a2 + b + 11b2 – 6
Add or subtract
the coefficients.

11. Simplify the algebraic expressions.
Example B
Simplify the algebraic expressions.
2(x2 – 13x) + 6
2x – 26x + 6 2
Distributive Property.
There are no like terms to combine.

12. Practice on your own:
Simplify the algebraic expressions.