Luttrell 2012
114
Name: ______________________
Date: _____
8a – Multiplying Polynomials
If the teacher were to ask the class to multipl
y
2
x
+ 5 to
x
- 3, many students will give the
incorrect answer of 2
x
2
- 15. These students didn’t distribute correctl
y
, causing them to lose the
middle terms. There are four methods to ensure a complete answer: traditional distribution, box
method, FOIL, or multipl
y
ing like you did with real numbers. The letters of FOIL stand for the
product of first terms, outer terms, inner terms, and last terms of each binomial. The box method
uses a multiplication table or a Punnett Square (see biolog
y
class) with the binomials. The
answer for both methods is the sum of these products.
Traditional distribution
: (2
x
2
+ 4)(
x
- 1) = (2
x
2
+ 4)
x
+ (2
x
2
+ 4)(-1) = 2
x
3
- 2
x
2
+ 4
x
- 4
Box Method
:
x
-1
2
x
2
2
x
3
-2
x
2
4
4
x
- 4
F O I L
Multiply like Reals
:
(2
x
+ 5)(
x
- 3) = (2
x
)(
x
) + (-3)(2
x
) + (5)(
x
) + (5)(-3)
2
x
+ 5
= (2
x
2
) + (-6
x
) + (5
x
) + (-15)
×
x
- 3
= 2
x
2
- 6
x
+ 5
x
- 15
-6
x
- 15
= 2
x
2
-
x
- 15
2
x
2
+ 5
x
2
x
2
-
x
- 15
E
x
pand.
1. (
x
- 3
y
)(
x
+ 2
y
)
2. (
x
+5)
2
3. (
x
-2)(3-
x
)
4. (4
x
-3)(4
x
+3)
5. (2a+3b)(a-5b)
6. (
x
+ 2)(10 - 4
x
)
7. (W + 2)(W - 2) 8. (a - 4)(a + 4)
9. (11-
x
)(
x
+3)
10. (3
x
2
- 4)(
x
+ 2)
11.(
x
2
+ 2)(2
x
2
+ 1) 12. (2
x
2
- 6)(
x
2
+ 4)
