Activity
1. Show that and are equivalent expressions by drawing a diagram or applying the distributive property. Show your reasoning.
Compare your answer:
Drawing a Diagram:
The sum of the partial products are or .
Applying the Distributive Property:
Applying the distributive property to gives .
2. For each expression, write an equivalent expression. Show your reasoning.
a.
Compare your answer:
b. . For example, applying the distributive property to gives , which equals .
c.
Compare your answer:
, because .
Or using a diagram:
Adding the partial products in the four sub-rectangles gives , which equals .
Compare your answer:
, because .
Video: Finding Products of Differences
Watch the following video to learn more about finding products of differences.
Self Check
Additional Resources
Multiplying Binomials with Negative Numbers
In a previous lesson, you learned how to square a binomial.
and
You can use this to solve the following example.
Example 1
Find the expression equivalent to .
This means to multiply by . So, .
Now, distribute. Remember, you can use FOIL.
Distribute the to the second binomial, then distribute the to the second binomial.
Then, combine like terms.
The expression becomes .
Example 2
Find the expression equivalent to .
First, distribute. Remember, you can use FOIL.
Multiply the by , then multiply the by and combine like terms:
Try it
Try It: Multiplying Binomials with Negative Numbers
Find the expression equivalent to .
Here is how to find an equivalent expression:
Distribute the to , and then distribute the to . Remember, you can use FOIL.
Next, combine like terms.