R2
Factoring
R5
CAUTION

Avoid
the
common
error
of
writing
(x
+
y)?
=
x>
+
y2.
As
the
first
step
of
Example
5
shows,
the
square
of
a
binomial
has
three
terms,
so
e+
y)2
=x*
+
2xy
+'y2.'«\
3
Furthermore,
higher
powers
of
a
binomial
also
result
}n
more
than
two
terms.
For
example,
verify
by
multiplication
that
(x
+
y)3
=x>+
3%y
+
3xy®
+
¥
Remember,
for
any
value
of
n
#
1,
(x
+
y)"
#x"
+
y"
R.
Exercises
Ferform
the
indicated
operations.
15.
3p
—
)(9p*
+3p
+
1)
1022
—
6x
+
L1)
+
(=32
+
7x
—
2)
16.
(3p
+2)(5p*
+p
—
4)
242
—3y+8)

(P
—6y—2)
17.
(2m
+
1)(4m®
—
2m
+
1)
3
6(2¢°
+
4
—
3)
+
4(¢*
+
7q
—
3)
18.
(k
+
2)(12K*
—
3K*
+
k
+
1)
220372
+
dr
+2)
=
3(—rF
+4r
=
5)
19.
(x+y+2)Bx—
2
—2)
5
0613x%
—
4215x
+
0.892)
—
047(2x*
—
3x
+
5)
20.
(r
+
2s
=
30)(2r
—
25
+
1)
£
05(572
+32r—6)
—
(1772
=
2r
—
1.5)
21,
(x
+
1)(x
+
2)(x
+
3)
=
—om(2m®
+
3m
—
1)
22,
(x
—
D(x
+
2)(x

3)
£
ar
=20
+
50+
6)
23.(x
+2)°
83—
2y)(3t
+
5y)
24.
(2a
—
4b)?
18
ok
+
q)(2k
—
q)
25.
(x
—
)
2
—3x)(2
+
3x)
26.
(3x
+y)*
s
=
5)(6m
—
5)
YOUR
TURN
ANSWERS
s
1.
—9x*
+
8x
+
13
2.12)°
+
29>
—
19y
—
10
3.6x°
4+
19x
—
7
4.
27x°
+
54x%y
+
36xy°
+
8y*
R.2
Factoring
Multiplication
of
polynomials
relies
on
the
distributive
property.
The
reverse
process,
where
a
polynomial
is
written
as
a
product
of
other
polynomials,
is
called
factoring.
For
example,
one
way
to
factor
the
number
18
is
to
write
it
as
the
product
9

2;
both
9
and
2
are
factors
of
18.
Usually,
only
integers
are
used
as
factors
of
integers.
The
number
18
can
also
be
written
with
three
integer
factors
as
2+
3«
3.
The
Greatest
Common
Factor
To
factor
the
algebraic
expression
15m
+
45,
first
note
that
both
15m
and
45
are
divisible
by
15;
15m
=
15+
m
and
45
=
15+
3.
By
the
distributive
property,
15m
+
45
=15m
+
153
=
15(m
+
3).