1.2 Use the language of algebra  (Page 5/18)

Indentify and combine like terms

Algebraic expressions are made up of terms. A term is a constant, or the product of a constant and one or more variables.

Examples of terms are $7,y,5x^2,9a,\text{and}{b}^5.$

The constant that multiplies the variable is called the coefficient .

Think of the coefficient as the number in front of the variable. The coefficient of the term 3 x is 3. When we write x , the coefficient is 1, since $x=1·x.$

Some terms share common traits. Look at the following 6 terms. Which ones seem to have traits in common?

The 7 and the 4 are both constant terms.

The 5x and the 3 x are both terms with x .

The $n^2$ and the $9n^2$ are both terms with $n^2.$

When two terms are constants or have the same variable and exponent, we say they are like terms .

• 7 and 4 are like terms.
• 5 x and 3 x are like terms.
• $x^2$ and $9x^2$ are like terms.

Adding or subtracting terms forms an expression. In the expression $2x^2+3x+8,$ from [link] , the three terms are $2x^2,3x,$ and 8.

If there are like terms in an expression, you can simplify the expression by combining the like terms. What do you think $4x+7x+x$ would simplify to? If you thought 12 x , you would be right!

Add the coefficients and keep the same variable. It doesn’t matter what x is—if you have 4 of something and add 7 more of the same thing and then add 1 more, the result is 12 of them. For example, 4 oranges plus 7 oranges plus 1 orange is 12 oranges. We will discuss the mathematical properties behind this later.

Simplify: $4x+7x+x.$

Add the coefficients. 12 x

How to combine like terms

Simplify: $2x^2+3x+7+x^2+4x+5.$

Solution

Got questions? Get instant answers now!

Got questions? Get instant answers now!