Download 3.2.3 Multiplying Polynomials and the Distributive Property Name: I

3.2.3 Multiplying Polynomials and the Distributive Property
Name:_____________________________
I can: ____________________________________________________________________________________.
Double Distributive Property or FOIL - can only be used to multiply two binomials
Example: Multiply (3x – 4) ( x + 2).
Example: Multiply (–5x + 7) (–3x – 6)
Generic Rectangle - can be used to multiply any polynomials
(factor 1)
Example: Multiply (2x – 4) (–3x2 + 5x – 6)
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(factor 2)
Example: Multiply (–x + 3)2
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Example: Multiply 3x(x2 + 7x – 5)
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Practice
Use the Distributive Property(FOIL) to multiply the following;
1. (x + 3)(x + 8)
2. (y – 4)(y + 7)
3. (3y) (x – y)
4. (2x)(x – 1)
5. (2r – 5)(r + 3)
6. (3x + 1)(5x – 3)
7. (x – 3)2
8. (5t – 1)(3t – 2)
9. (a + 11)(11a + 1)
Use Generic Rectangles to multiply the following;
1. (4x – 7) (2x – 9)
2. (4x + 3) (7x – 5)
3. (–3x + 5)2
4. (x + 2)(4x – 3)
5. (4x – 7)2
6. (3x – 5) (2x2 – 4x + 7)
7. (4x + 3) (3x2 – 5x – 6)
8. (2x2 – 5x) (9x2 + 6x + 4)
9. (2x2) (3x2 + 5x - 4)
The Generic Rectangle Challenge - Find the missing terms and write area in factored form = area as sum
1.
2.
-3
____
x
2x2
_____
_____
3.
+5
____________________ = ____________________
-2
-5x2
_____
3x3
x2
+1
5.
-16x
+4
_____
____________________ = ____________________
_____
+5
____________________ = ____________________
6.
+7
____
5x
_____
4.
____
x
27x3
9x2
+1
____________________ = ____________________
-18x
-2
-15x2
_____
_____
+1
____________________ = ____________________
+16x
+16
12x4
4x2
_____
+12
____________________ = ____________________
3-57 CLOSED SETS Do you remember the subsets of REAL numbers?
Whole numbers (positive integers and zero) are said to be a closed set under addition:
 If you add two whole numbers, you always get a whole number.
15 + 23 = 38 a whole number (This is an example that proves the point)
On the other hand, whole numbers are not a closed set under subtraction:
 If you subtract two whole numbers you may not get a whole number:
15 – 23 = –8 an integer
(This is a counter-example that disproves the point.)
Answer the following questions;
1. Are whole numbers a closed set under multiplication? Use examples and counter-examples to explain.
2. Are whole numbers a closed set under division? Use examples and counter-examples to explain.
Now, use the same process to examine integers and closed sets.
1. Are integers a closed set under addition? Use examples and counter-examples to explain.
2. Are integers a closed set under subtraction? Use examples and counter-examples to explain.
3. Are integers a closed set under multiplication? Use examples and counter-examples to explain.
4. Are integers a closed set under division? Use examples and counter-examples to explain.