# Polynomial Multiplication Worksheets

Polynomials are algebraic expressions that consist of several terms. Each term often contains different powers of the same variable(s). The name often haunts students, but the problems associated with the, especially operations, are no more difficult than working with larger numbers in operations. It all begins and ends with the ability of the student to stay organized through the process and being able to spot like terms. This particular operation is used often in the construction industry to determine the desired dimensions of a structure that will be fabricated. It is also essential when constructing and engineering any type of curved structure. These worksheets and lessons help students learn how to multiply polynomials.

### Aligned Standard: HSA-APR.A.1

- Polynomial Product Step-by-step Lesson-We work through your first polynomial product and help you solve them as a series.
- Guided Lesson - These are three problems on polynomials that are very common to see. You might even recognize the common pattern that is used for these.
- Guided Lesson Explanation - Work with the concept of (FOIL) First-Outside-Inside-Last for solving these.
- Practice Worksheet - I threw a couple in there with three terms to give you a bit of a challenge.
- Matching Worksheet - Match the polynomial products to their final outcome.
- Multiplying Polynomials Five Pack - A rapid fire splash of problems for you to practice with. These problems are the standard level you will see.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Once again, get the kids in the habit of treating polynomials like a three or more part equation.

- Homework 1 - In algebra when we use the distributive property, we are expanding or distributing.
- Homework 2 - Now, multiply the third bracket with the product of first and the second bracket.
- Homework 3 - We will multiply both the parentheses.

### Practice Worksheets

Remind students that spacing these problems is critical when solving them.

- Practice 1 - Find the product of the polynomials.
- Practice 2 - (5x + 2) (5x - 5)
- Practice 3 - What is the final value left behind?

### Math Skill Quizzes

I threw a couple of curve balls in here to keep kids on their toes.

- Quiz 1 - Find the products.
- Quiz 2 - We add exponents in this quiz.
- Quiz 3 - The zero value always throws them off.

### How to Multiply Polynomials

2 x 2 + 3y +4z

We all have seen an expression or a mathematical statement like the one above. Such combinations of variables (letters like x, y, z), constants (numbers like 2, 3, 4) and exponents (like 2 in x^{2}) are known as polynomials. Polynomials contain operators like: multiplication, addition, subtraction, and positive exponents. But they don't have division operators or negative exponents.

Here, we are going to focus on the multiplication operator with polynomials. There are a couple of things you need to keep in mind when multiplying polynomials with each other:

**Step 1 -** Multiply each term in one polynomial by each term in the other polynomial.

**Step 2 -** Combine those terms and simplify if needed.

Let's begin with the easiest of the bunch and work our way up the spectrum.

** Monomial With Monomial (1 Term Times 1 Term)** - To multiply a monomial with monomial, we first multiply the coefficients (multipliers) then the variables and find the result.

(3a) (4ab)

(3 . 4) (a . a) (b) : Place like terms together.

12 a^{2}b: Note that when multiplying variables, we add their exponents.

** Monomial With Binomial (1 Term Times 2 Terms)** - Multiply the single term with each of the two terms of binomial. For example,

(a^{2} - a) 2b

(a^{2} -. 2b) - (a. 2b)

2a^{2} b - 2ab

** Binomial With Binomial (2 Terms Times 2 Terms)** - This one is a bit longer than the first two types of polynomial multiplication. In this multiplication, each of the two terms in one binomial is multiplied with each of the two terms in the other binomial.

To elaborate with an example, (a + b) (c +d)

Taking the first binomial: a.c + a.d + b.c + b.d = ac + ad + bc +bd

You can multiply the binomials in any order, make sure that each of the first two terms is being multiplied by each second term of the binomials.