Expressions, Equations, and Functions
COMBINING LIKE TERMS
Algebraic expressions can also be simplified by combining (adding or subtracting) terms that
have the same variable(s) raised to the same powers, into one term. The skill of combining like
terms is necessary for solving equations. For additional information, see the Math Notes box in
Lesson 6.2.4 of the Core Connections, Course 1 text, Lesson 4.3.2 of the Core Connections,
Course 2 text, or Lesson 2.1.3 of the Core Connections, Course 3 text. For additional examples
and practice, see the Core Connections, Course 2 Checkpoint 7A materials.
Example 1
Combine like terms to simplify the expression 3x + 5x + 7x.
All these terms have x as the variable, so they are combined into one term, 15x.
Example 2
Simplify the expression 3x + 12 + 7x + 5.
The terms with x can be combined. The terms without variables (the constants) can also be
combined.
3x + 12 + 7x + 5
3x + 7x + 12 + 5 Note that in the simplified form the term with the variable is listed
before the constant term.
10x + 17
Example 3
Simplify the expression 5x + 4x2 + 10 + 2x2 + 2x 6 + x 1.
5x + 4x2 + 10 + 2x2 + 2x 6 + x 1 Note that terms with the same variable but
with different exponents are not combined and
4x2 + 2x2 + 5x + 2x + x + 10 6 1
are listed in order of decreasing power of the
6x2 + 8x + 3 variable, in simplified form, with the constant
term last.
Parent Guide with Extra Practice 1
Example 4
The algebra tiles, as shown in the Perimeter Using Algebra Tiles section, are used to model how
to combine like terms.
The large square represents x 2 , the rectangle represents x, and the small square represents one.
We can only combine tiles that are alike: large squares with large squares, rectangles with
rectangles, and small squares with small squares. If we want to combine:
2x2 + 3x + 4 and 3x2 + 5x + 7, visualize the tiles to help combine the like terms:
2x2 (2 large squares) + 3x (3 rectangles) + 4 (4 small squares)
+ 3x2 (3 large squares) + 5x (5 rectangles) + 7 (7 small squares)
The combination of the two sets of tiles, written algebraically, is: 5x2 + 8x + 11.
Example 5
Sometimes it is helpful to take an expression that is written horizontally, circle the terms with
their signs, and rewrite like terms in vertical columns before you combine them:
(2x2 5x + 6) + (3x2 + 4x 9)
2x 2 5x + 6 + 3x 2 + 4x 9
2x 2 ! 5x + 6 This procedure may make it easier to
identify the terms as well as the sign of
+ 3x 2 + 4x ! 9 each term.
5x 2 ! x ! 3
Problems
Combine the following sets of terms.
1. (2x2 + 6x + 10) + (4x2 + 2x + 3) 2. (3x2 + x + 4) + (x2 + 4x + 7)
3. (8x2 + 3) + (4x2 + 5x + 4) 4. (4x2 + 6x + 5) (3x2 + 2x + 4)
5. (4x2 7x + 3) + (2x2 2x 5) 6. (3x2 7x) (x2 + 3x 9)
7. (5x + 6) + (5x2 + 6x 2) 8. 2x2 + 3x + x2 + 4x 3x2 + 2
9. 3c2 + 4c + 7x 12 + (4c2) + 9 6x 10. 2a2 + 3a3 4a2 + 6a + 12 4a + 2
Answers
1. 6x2 + 8x + 13 2. 4x2 + 5x + 11 3. 12x2 + 5x + 7 4. x2 + 4x + 1
5. 6x2 9x 2 6. 2x2 10x + 9 7. 5x2 + 11x + 4 8. 7x + 2
9. c2 + 4c + x 3 10. 3a3 2a2 + 2a + 14
2 Core Connections, Courses 13
