Technical Mathematics, Sixth Edition

2.2. Adding and Subtracting Polynomials

Now that we know some of the language of algebra, let's go on to the basic operations. We will start with addition and subtraction. We will see that much of what we learned in Chapter 1 about adding and subtracting numbers (rules of signs, commutative law, and so forth) applies here as well.

2.2.1. Polynomials

Recall that an algebraic expression in which the power of every variable is a positive integer is called a polynomial.

Example 17: Some polynomials are 3x4, 4x2 − 5x − 4, 2xy + y3, and 7 Some expressions that are not polynomials are

2.2.2. Combining Like Terms

Terms that differ only in their coefficients are called like terms. Their variable parts are the same.

Example 18: Here are some like terms. 4xz and −5xz are like terms. 3x2y3 and 7xy3 are like terms.

We add and subtract algebraic expressions by combining like terms. Like terms are added by adding their coefficients. We also call this collecting terms.

Example 19: These examples show the combining of like terms. 3y + 4y = 7y 18z − 9z = 9z 7x2 + 3x2 = 10x2

Don't forget that any term with no numerical coefficient has an unwritten coefficient of 1.

Example 20: More examples of combining like terms. 4x + x = 4x + 1x = 5x −3y + y = −3x − 1y = −2y 2z2 + z2 = 2z2 + 1z2 = 3z2

2.2.3. Commutative Law of Addition

The commutative law for addition simply states that you can add quantities ...