Home > Grade Levels > High School Algebra >

## Polynomial Multiplication

#### 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  #### 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.

#### 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.