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| Math Central | Quandaries & Queries |
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Question from Maddie, a student: How Would I Answer This Problem? Name The coefficients, any like terms, and any constants.
I Would Really Appreciate It If You Could Help Me |
Hi Maddie,
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
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