Let’s start this lesson with a few things that you’ll have to understand before we start adding and subtracting. A polynomial is an expression with more than one term. So what’s a term? A term can be a few things. It can be just a number like:

4                                 -23                              .5                                100,000,001

These all qualify as single terms. A term can also be a variable like:

x                                  b                                  g2                                y3

Lastly, a term can be a collection of the above. This would include:

xy2                              45ab2c                                   9dx3                           3.14r2

An addition or a subtraction sign separates terms.

This is one term, or a monomial:                                   6ab2

This would be two terms, or a binomial:                       4xy + 8z

This would be three terms, or a trinomial:                    d2 + 4d – 3

How many terms does the following have?

-5x2 – 14x3y + 4xy3 + 11x3

There are four terms!

Ok, got that out of the way! Now, let’s talk about something known as “like terms”. When terms are alike, they can be combined. Terms can be combined when the variables and the exponents of those variables are exactly alike. For example:

Alike:                       4x2y and -3x2y                      5a2b3c and 2a2b3c                    -4 and 6

Not Alike:                -3x2y and 2xy                       3a2b3c and 5a3b2c                   6yz and 6z

When terms are alike, we can add them together. Here is an example:

(-8x4 – 12x3y) + (-5x4 – 14x3y + 4xy3) + (-7xy3 – 4x3y)

Let’s highlight “like terms” with the same colors.

(-8x4 – 12x3y) + (-5x4 – 14x3y + 4xy3) + (-7xy3 – 4x3y)

We combine these by keeping the variables exactly the same but adding the coefficients (the number in front of the variable) and end up with:

-13x4 – 30x3y - 3xy3

Answer: -13x4 – 30x3y - 3xy3

And that’s all there is to adding polynomials! When we subtract polynomials, it adds one extra step. When there is a minus sign in front of the parenthesis, we can change it to addition as long as we change every sign in the parenthesis as well. We are technically distributing a “-1” into the parenthesis. For example:

(5x3 + 8x4y) – (-7x3 – 3x2y2 + 12x4y4) + (-7x2y2 – 11x3)

The second polynomial has a subtraction sign in front, so let’s change that.

(5x3 + 8x4y) + (7x3 + 3x2y2 - 12x4y4) + (-7x2y2 – 11x3)

Now, let’s locate “like terms”:

(5x3 + 8x4y) + (7x3 + 3x2y2 - 12x4y4) + (-7x2y2 – 11x3)

If a term doesn’t have any like terms, then it just stays the same value.

x3 + 8x4y - 4x2y2 - 12x4y4

Answer: x3 + 8x4y - 4x2y2 - 12x4y4

2808 x

Simplify each expression.

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2532 x

Simplify each expression.

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2409 x

Simplify each expression.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

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### Geometry

Circles
Congruent Triangles
Constructions
Parallel Lines and the Coordinate Plane
Properties of Triangles

### Algebra and Pre-Algebra

Beginning Algebra
Beginning Trigonometry
Equations
Exponents
Factoring
Linear Equations and Inequalities
Percents
Polynomials