Multimedia Link: For further help, visit http://www.purplemath.com/modules/polydefs.htm – Purplemath’s website – or watch this CK-12 Basic Algebra: Adding and Subtracting Polynomials
A binomial is a polynomial with two terms. The Distributive Property also applies for multiplying binomials. Let’s think of the first parentheses as one term. The Distributive Property says that the term in front of the parentheses multiplies with each term inside the parentheses separately. Then, we add the results of the products.
We see that we can apply the Distributive Property on each of the parentheses in turn.
What you should notice is that when multiplying any two polynomials, every term in one polynomial is multiplied by every term in the other polynomial.
Solution: We must multiply each term in the first polynomial with each term in the second polynomial. First, multiply the first term in the first parentheses by all the terms in the second parentheses.
Now we multiply the second term in the first parentheses by all terms in the second parentheses and add them to the previous terms.
Now we can simplify.
Solving Real-World Problems Using Multiplication of Polynomials
We can use multiplication to find the area and volume of geometric shapes. Look at these examples.
Find the area of the following figure.
Find the volume of the following figure.
Now, multiply the two binomials together.
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Multiplication of Polynomials (9:49)
Multiply and simplify.
Find the areas of the following figures.
Find the volumes of the following figures.
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