Luttrell 2012
119
Name: ______________________
Date: _____
8f – Difference of Squares
When a quadratic e
x
pression of
ax
2
±
bx
±
c
is missing the b
x
, it probably still can be factored.
As you noted before in a previous lesson,
x
2
-
c
can factored into (
x
- d)(
x
+ d). Then it can be
concluded
c
is a perfect square. The factors of c are equal, so when foiling d
x
- d
x
= b
x
= 0.
E
x
ample A:
x
2
- 49 = (
x
- 7)(
x
+ 7).
Check work:
x
2
-7x +7x
- 49
can be simplified to
x
2
- 49.
A leading coefficient must be factored into equal quantities as well.
E
x
ample B: 9
x
2
- 100 = (3
x
- 10)(3
x
+ 10)
Ma
y
be
y
ou can simplif
y
before factoring
E
x
ample C: 25
x
2
- 100 = 25(
x
2
- 4) = 25(
x
- 2)(
x
+ 2)
Summarize the following factor rules:
Perfect Trinomial
a
2
x
2
± 2ab
x
+
b
2
=
Difference of Squares
a
2
x
2
-
b
2
=
Solve b
y
factoring:
1.
x
2
- 9 = 0
2.
x
2
= 16
3.
x
2
- 25 = 0
4.
x
2
- 36 = 0
5. 25
x
3
- 100
x
= 0
6. 2
x
3
- 32
x
= 0
7. 3
x
2
- 27 = 0
8. 4
x
2
- 36 = 0
9. 25
x
2
- 9 = 0
