Combining like terms: Whole number coefficients

A term is a constant or a combination of variables in an expression.

For example, in the equation 15 + 3x3 + 2x = 9x - 4,

the terms on the left are 15, 3x3 and 2x, while the terms on the right are 9x, and -4.

Terms in algebraic expressions that have the same variable(s) with same exponents are called like terms.

Combining Like Terms is a method used to simplify an expression or an equation using addition and subtraction of the coefficients of terms.

Consider the expression below

8 + 9

By adding 8 and 9, we can easily find that the expression is equivalent to 17.

Algebraic expressions can be simplified by combining like terms. Consider the algebraic expression below:

18x + 13 + 9x

We see that 18x and 9x are like terms. Therefore, the coefficients, 18 and 9, can be added.

18x + 9x = 27x

So, 18x + 13 + 9x = 27x + 13

Rules to combine like terms

  • We simplify algebraic expressions and equations by combining like terms.

  • First, we identify sets of like terms.

  • Now the coefficients of each set of like terms are added.

  • With the like terms combined, the expression becomes simplified

  • algebraic equations become easier to be solved

Simplify the following expression by combining like terms:

2x − 10y − 18x + 18y + 21x

Solution

Step 1:

Combining like terms

2x − 10y − 18x + 18y + 21x

= (2x −18x + 21x) + (−10y + 18y)

Step 2:

(2x −18x + 21x) + (−10y + 18y) = 5x + 8y

Step 3:

So, 2x − 10y − 18x + 18y + 21x

= 5x + 8y

Simplify the following expression by combining like terms:

12a + 8b + 9c + 5a + 7b + 11c

Solution

Step 1:

Combining like terms

12a + 8b + 9c + 5a + 7b + 11c

= (12a + 5a) + (8b + 7b) + (9c + 11c)

Step 2:

(12a + 5a) + (8b + 7b) + (9c + 11c)

= 17a + 15b + 20c

Step 3:

So, 12a + 8b + 9c + 5a + 7b + 11c

= 17a + 15b + 20c

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