#### Algebra - Combining Like Terms

Note: the “^” denotes an exponent; x^3 stands for x to the third power

Terms are the parts that make up an expression such as 5x^ 2 + 3x + 4. 5x^2, 3x and 4 are considered terms. However they are not alike. The examples below show examples of like terms:

5x^2, 6x^2, 3x^2, 9x^2 - They are alike because each term has “x” raised to the second power.

3x, 4x, 5x, 2x, 72x – These are alike because they all have an x variable.

1, 7, 22, 5, 4 – These terms are alike because each term has no variable…also, referred to as constants.

Also keep in mind:
*The numbers in front of the variables are the coefficients. i.e. 4x – “4” is the coefficient and ‘x” is the variable
* A variable without a coefficient has an implied coefficient of 1.

In order to simplify an expression,
1. Combine or group like terms.
2. Add or subtract the coefficients

Example 1:
Simplify: 4x – 6 – 2y + 3x + 14 + 5y + 8

1. Combine/Group like terms
4x + 3x -2y + 5y – 6 + 14 + 8

2. Add or Subtract the coeffiecients
7x +3y + 16

Thus, 4x – 6 – 2y + 3x + 14 + 5y + 8 = 7x +3y + 16

Example 2:
Simplify the expression: 4(x – 5) + 3x

1. Use the distributive property
4x – 20 + 3x

2. Combine/Group like terms
4x + 3x + 20

7x +20

Thus, 4(x – 5) + 3x = 7x +20

Example 3:
Simply the expression: 6x^2 – 3(x – 5x^2)

1. Use the distributive property
6x^2 – 3x – 15x^2

2. Combine/Group like terms
6x^2 – 15x^2 -3x

-9x^2 – 3x

Thus, 6x^2 – 3(x – 5x^2) = -9x^2 – 3x

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