## Polynomial Multiplication

#### Aligned To Common Core Standard:

**High School** - HSA-APR.A.1

How to Multiply Polynomials?
2x2 + 3y +4z
We all have seen an expression or a mathematical statement like the one above.
Such combinations of variables (alphabets like x, y, z), constants (numbers like 2, 3, 4) and exponents (like 2 in x2) are known as polynomials. Polynomials contain multiplication, addition, positive exponents and subtraction. But they don't have division and negative exponents
Here, we are going to focus on the multiplication of polynomials
Multiplication of Polynomials
There are a couple of things you need to keep in mind when multiplying polynomials with each other
- Multiply each term in one polynomial by each term in the other polynomial
- Add those terms and simplify if needed
Let's begin with the easiest one
**MONOMIAL WITH MONOMIAL (1 TERM TIMES 1 TERM)** -
To multiply a monomial with monomial, we first multiply the coefficients (constants) then the variables and find the result
(3a) (4ab)
(3.4) (a. ab)
12 a^2b,
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,
(a2 – a) 2b
(a2. 2b) – (a. 2b)
2a2b – 2ab
**BINOMIAL WITH BINOMIAL (2 TERMS TIMES 2 TERMS)** -
This one is a bit longer than the first two kinds 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. These worksheets and lessons help students learn how to multiply polynomials.

### Printable Worksheets And Lessons

- 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.

#### 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.