**Introduction to Addition and Subtraction of Terms**

*I'm an algebra liar. I figure two good lies make a positive*.

–Tim Allen (1953– ) American Entertainer

In this lesson, you'll learn how to combine a pair of signs into one sign, and how to add and subtract like terms.

**When we add** two whole numbers or subtract one whole number from another, we only have to work with one sign, either a plus sign or a minus sign. **Integers** are all of the whole numbers, their negatives, and zero. When we add two integers, we often have to work with two or more signs. Sometimes in an integer addition or subtraction problem, two signs appear right next to each other: 2 + –3.

We can combine a pair of signs into one sign according to the following chart:

In other words, if the two signs are different, replace them with the minus sign. If two signs are the same, replace them with a plus sign. 2 + –3 becomes 2 – 3, since the two signs between 2 and 3 are different. 4 + (+6) becomes 4 + 6, and 3 – (–7) becomes 3 + 7.

**Adding Like Terms**

Remember, like terms have the same base, and those bases have the same exponents. To add two like terms, we add the coefficients of the terms and keep the base and its exponent. Let's say we want to add 4*x*^{3} and 3*x*^{3}. First, we check that the terms are like terms. Because both have a base of *x* and an exponent of 3, these are like terms. Next, add the coefficients of the terms. The coefficient of 4*x*^{3} is 4 and the coefficient of 3*x*^{3} is 3. 4 + 3 = 7. Our answer has the same base and the same exponent as the bases and exponents of the terms that we have added, so 4*x*^{3} + 3*x*^{3} = 7*x*^{3.}

Do not forget to write the base and exponent of your answer. Once you are sure that you are adding like terms, write the base and the exponent of your answer right away. Before finding the sum of 13 |

To find –8*u*^{8} + (+6*u*^{8}), we must combine a pair of signs. Because + and + are the same sign, they can be combined into a single plus sign. –8*u*^{8} + (+6*u*^{8}) = –8*u*^{8} + 6*u*^{8}. The base of these terms is *u* and the exponent is 8, so the base and exponent of our answer is *u*^{8}. Add the coefficients: –8 + 6 = –2, so –8*u*^{8} + 6*u*^{8} = –2*u*^{8.}

**Subtracting Like Terms**

Just as with addition, to subtract one like term from another, we work with the coefficients of the terms. Our answer has the same base and the same exponent as the term we are subtracting and the term from which we are subtracting. To find the difference between two like terms, subtract the coefficient of the second term from the coefficient of the first term: 8*x*^{7} – 3*x*^{7} = 5*x*^{7}.

What is –6*e*^{3} – (+4*e*^{3})? First, check that we have like terms. Both terms have a base of *e* and an exponent of 3, so we are ready to subtract. Next, combine the two different signs into a single minus sign: –6*e*^{3} – (+4*e*^{3}) = –6*e*^{3} – 4*e*^{3}. Now, subtract 4 from –6: –6 – 4 = –10, so –6*e*^{3} – 4*e*^{3} = –10*e*^{3.}

**Adding and Subtracting Unlike Terms**

This might be the shortest topic in this book—because you cannot add or subtract unlike terms. The terms 6*x* and 2*x*^{2} cannot be added, and 2*ab* cannot be subtracted from 10*x*^{3}*y*. If you see 8*y*^{3} + 2*y*6 or 9*m*^{6} – 4*a*, you must leave those terms just as you found them. They cannot be combined. This is why you must always check that you have like terms before adding or subtracting.

Find practice problems and solutions for these concepts at Addition and Subtraction of Terms Practice Questions.

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