Multiplying Polynomials – Examples Page
Look at these multiplying polynomials examples to prepare for your math exam.
Multiplying Polynomials – Quiz
Instructions: Multiply the polynomials in the questions in the quiz below. To see the free samples first, please scroll down.
[WpProQuiz 21]
Multiplying Polynomials – Example
A polynomial contains two or more algebraic terms, so you will need to know how to multiply the terms of the polynomial together to get the correct result. Now look at the example that follows.
Instructions: Simplify the following expression.
3a2b(3ab + 4a2b2 – 5ab)
Answer: 12a4b3 – 6a3b2
STEP 1: Set up the distribution of the multiplication.
3a2b(3ab + 4a2b2 – 5ab) =
(3a2b × 3ab) + (3a2b × 4a2b2) + (3a2b × –5ab)
STEP 2: Multiply one term by the other in each set of parentheses.
Multiply the numbers by each other and the variables by each other, paying attention to the exponents and negatives.
(3a2b × 3ab) + (3a2b × 4a2b2) + (3a2b × –5ab) =
9a3b2 + 12a4b3 + –15a3b2
STEP 3: Simplify further by grouping like terms together, if possible.
9a3b2 + 12a4b3 + –15a3b2 =
9a3b2 + 12a4b3 – 15a3b2 =
9a3b2 – 15a3b2 + 12a4b3 =
–6a3b2 + 12a4b3 =
12a4b3 – 6a3b2
Multiplying Polynomials – Step by Step
Multiplying polynomials is performed by using the distributive property of multiplication.
Polynomials include quadratics, binomials, trinomials, and polynomials with more than three terms.
You will usually have to deal with exponents in order to solve polynomial multiplication problems.
So, be sure that you are comfortable with Exponent Laws for these types of algebra questions.
You may see the words “simplify” or “expand” in the instructions when you have problems on multiplying polynomials.
“Simplify” and “expand” both mean that you have to perform multiplication on the polynomial.
When multiplying polynomials, you need to multiply one term by the other in each set of parentheses. To do so, multiply the numbers by each other and the variables by each other. Be sure to pay special attention to the exponents and negatives.
If you have had difficulties with this example on multiplying polynomials, please view our posts on:
Multiplying Polynomials – Further Practice
Multiplying polynomials in quadratic equations is performed by using the FOIL Method.
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