Chapter 6 FaCtoring and the distributive ProPerty 141
3.
34
5
2 34
5
2
1
34
5
2
1
5
5
x 342
x
x
x
x
x
x
x
− xx
+
−= −
+
−= −
+
−⋅+
+
= −−( ++
+
= −− −
+
= −
+
5
5
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5
14
5
)
x
xx
x
x
x
- x
xy
y
xy
x
x
xy
xy
y
xy
xy
xy
x
23425
34
34 34
2
+ 2
+
−
=
+
⋅ −
−
+
−
⋅ +
+
= (()()
()()(
34 2
342
342
3
xyyxy^22
xyxy
xxyxyy
x
−+ +
−+
= −++
−−+
= −+
−+
42
32
342
22
yxy
xxyy
xyxy
)( )
()()
- xx xx xx xx xx xx
xx
636363
63
6363
63
63
6
+
+
−
=
+
⋅ −
−
+
−
⋅ +
+
= ( −^3363
6363
6363
636
)( )^22
()()()(
++
−+
= −++
−+
xx
xx
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xx 33
12
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)
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=
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x
xx
Factoring
The distributive property, a(b + c) = ab + ac, can be used to factor a quan-
tity from two or more terms. In the formula ab + ac = a(b + c), a is fac-
tored from (or divided into) ab and ac on the right side of the equation.
The first step in factoring is to decide what quantity to factor from each
term. The second step is to write each term as a product of the factor and
something else (this step will become unnecessary once you are experi-
enced). The last step is to apply the distributive property in reverse. An
expression is “completely factored” if that the terms inside the parentheses
have no common factor (other than 1). For instance, 8(2x + 3) is com-
pletely factored because 2x and 3 have no common factors (other than 1).
The expression 4(15x + 10) is not completely factored because 5 divides
both 15x and 10.
