Combining pke 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 pke terms.

Combining Like Terms is a method used to simppfy 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 simppfied by combining pke terms. Consider the algebraic expression below:

18x + 13 + 9x

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

18x + 9x = 27x

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

Rules to combine pke terms

We simppfy algebraic expressions and equations by combining pke terms.

First, we identify sets of pke terms.

Now the coefficients of each set of pke terms are added.

With the pke terms combined, the expression becomes simppfied

algebraic equations become easier to be solved

Simppfy the following expression by combining pke terms:

2x − 10y − 18x + 18y + 21x

Solution

Step 1:

Combining pke 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

Simppfy the following expression by combining pke terms:

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

Solution

Step 1:

Combining pke 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