   SEARCH HOME Math Central Quandaries & Queries  Question from Maddie, a student:

How Would I Answer This Problem?

Name The coefficients, any like terms, and any constants.

Coefficients Like Terms Constants
3x+7
4m+(-3n)+n
6kp+9k+kp-14
-8y+6ab+7-3ba
c+2c+c-5c+1

I Would Really Appreciate It If You Could Help Me
Sincerely, I'm going to look at some different expressions. First of all consider 5x + y - 7.

The coefficients are the numbers that multiply the variables or letters. Thus in 5x + y - 7, 5 is a coefficient. It is the coefficient in the term 5x. Also the term y can be thought of as 1y so 1 is also a coefficient. Like terms are terms that contain the same variable raised to the same power. In 5x + y - 7 the terms are 5x, y and -7 which all have different variables (or no variables) so there are no like terms. Constants are terms without variables so -7 is a constant.

Now let's try 5a + 2b - 3a + 4. Here the coefficients are 5, 2 and -3. This time there are like terms, 5a and -3a and the constant is 4.

Finally, what about 4st - 5s + 3ts + 6? The coefficients are 4, -5 and 3 and the constant is 6. Since s times t is the same as t times s 4st and 3ts are like terms.

So here is the table for my three examples.

Coefficients Like Terms Constants
5x + 7y - 7 5, 7 none -7
5a + 2b - 3a + 4 5, 2, -3 5a, -3a 4
4st - 5s + 3ts + 6 4, -5, 3 4st, 3ts 6

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.