Practice 4-6

Practice 4.6 – Special Products
Name ____________________________________
When you multiply certain pairs of binomials, there is a pattern to the results. Use the distributive property and/or an area model to multiply and see if you notice anything special about the result. When looking for a pattern, try considering the following questions:
What do you notice about the answers?
What do they have in common?
Why do you think this happened?
Can you think of a shortcut to get the answer?
Pattern A
1. x  5 x − 5
2. x  3 x − 3
3. x  4x − 4
4. x − 2 x  2 
5. x − 6 x  6
6. x − y x  y 
7. Write down some observations about the results, then fill in the special product rule.
 A  B A − B =
8. Use this rule to write the answer directly.
a. x  9 x − 9
b. x − 8 x  8
c. 2 x  52 x − 5
d. 3 x  4 y 3 x − 4 y 
Pattern B – Use the distributive property and/or an area model to multiply and see if you notice anything special about the result.
1. x  7 x  7
2. x  2 x  2 
3. x  42 = x  4  x  4 
4. x  9 x  9
5. x  5 x  5
6. x  y  2 = x  y  x  y 
7. Write down some observations about the results, then fill in the special product rule.
8. Use this rule to write the answer directly.
a. x  6 x  6
b. 2 x  32 x  3 
2
 A  B =
Pattern C – Use the distributive property and/or an area model to multiply and see if you notice anything special about the result.
1. x − 7 x − 7
2. x − 2 x − 2 
4. Write down some observations about the results, then fill in the special product rule.
3. x − 42 = x − 4  x − 4 
5. Use this rule to write the answer directly.
a. x − 9 x − 9
b. 3 x − 13 x − 1
2
 A − B =

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