How to Add and Subtract Monomials and Polynomials

Algebra book containing algebraic expressions and terms.

Polynomials are mathematical expressions that consist of terms. Terms can simply be a number, a variable or the product of a variable and a number called a coefficient. Examples of terms include the following: 8x-6, 2x^2 +3x, y, 4. The coefficient in these terms is the number that you multiply by the variable. In this case the coefficients would be 8, 2, 3 and 1. A monomial is a type of polynomial that consists of one term like 2x. A polynomial that consists of two terms like 2x + 4 is called a binomial, and a polynomial made up of three terms like 3x^2 +2x + 8 is called a trinomial.

Instructions

Adding Polynomials

1. Combine like terms. For example, if you were asked to add (3x^2 +2x + 4) to (6x^2 + 4x + 8), you would combine 3x^2 with 6x^2, 2x with 4x and 4 with 8.

2. Add like terms. Arrange the terms vertically and add like this:

   3x^2 + 2x + 4

   + 6x^2 + 4x + 8.

3. Simplify. Your answer should then be 9x^2 + 6x + 12.

Subtracting Polynomials

1. Combine like terms. Just as you did with addition, group like terms together. For example, if you were asked to subtract (2x^3 + 8x + 6) from (3x^3 -2x + 4) you would combine 3x^3 with 2x^3, -2x with 8x and 4 with 6.

2. Subtract like terms. Arrange the like terms so they line up vertically as you did with addition and subtract.

   3x^3 - 2x + 4

   - 2x^3 + 8x + 6

3. Simplify. Your answer should then be x^3 - 10x - 2.

Adding and Subtracting Monomials

1. Combine like terms. For example, if you were asked to add 5x to 2x or subtract 2x from 5x, you would combine these terms as you did in the examples above.

2. Add or subtract the terms. In this case you would add 5x to 2x or subtract 2x from 5x.

3. Simplify. Your answer should then be 7x or 3x.

References

• WTMAU: Beginning Algebra Tutorial 27: Adding and Subtracting Polynomials
• Shahomwork: Adding and Subtracting Monomials and Polynomials