# Algebraic Expansion

```Algebraic Expansion
9/9/21
What
-
is
it
important
which
it
because
the
rule :
example
4C 5 t 6)
=
(4&times;5)+(4&times;6)
20 t 24
the
value
,
and
example
:
=
=
:
=
this is
4151-63
→
4417
=
true because
=
⇒ however with
(2077
⑦ X)
variables, YOU
2&times;-14
do CX 7)
cannot
-
-
5&times;-5+2&times;3
15&times;+10&times;2
since
&times;
therefore
distributive
you
rule
two
parts
44
ZCX -77
does
work
because it's
down the
rules
abt ac
=
to
unknown ,
is
using
law
expand the
expression
simply breaking
expression into
,
the
will allow
ofdoingcbtdtn-enmuitipiyinya.my
50 , this
cannot
expansion
44
=
example
acts t&Eacute;
:
=
another
know
variables
with
expression without
the
expressions
of
Cutlet W
general
variable
dealing
when
don't
simplify
easily
-
you
algebra?
expansion
=
why
brackets
involve
useful
is
and
1) algebraic expansion
2)
and
algebraic expansion
is
much
as
possible
.
as
-
the
PT
* general
Ca tb) Cctd)
rule :
FOIL
:
rule
first ,
act
=
outer, inner,
last → this
is
the order
↳
first
terms
X C
a
=
outer
terms
inner
terms
=
b X C
last
terms
=
b X d
example :
=
multiply
X d
=
a
to
81-27
(3-8)+(3-2) 1-(7-8)
C 3 + 7) C
+
=
24
=
100
6
+
56
t
+
G.27
14
-7
this
is
true because
.
(3+7) (81-2)
.
.
=
=
Variable
example
'
8b
you
you
2) ( 2b t
5)
'
t 20 b
8 bat
=
because
100
-
=
variables ,
t
CIO)
Ctb 2b)tC4b 5) 1- ( 2- 2b)
=
With
C4b
:
CIO) ✗
you
do
NEED to
24b
apply
t
do
cannot
not
1-
know
the
t
CZ
-
5)
4b t 10
10
cat b)
X
Cbt d)
the values ;
product
therefore
rule
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the
distributive
rule
twice
,
1) acct d)
then
2)
-
*
the
Curthose
rule :
general
example
Ca tb)
b)
( a-
(4+7) (4-7)
:
42
=
this
variable
↳
true
is
because
.
.
(4+7)
it
=
-33
-
8)
=
using
the
possible
not
8) j
CX
multiply
since the value
is
-
(4-7)
2✗
a
variables ,
unknown ,
49
CID ✗ C- 3)
=
with
72
=
CX + 8) CX
example :
-
b
-33
=
.
-
-
16
=
'
=
so,
it
can
difference
two
✗
-
of
82
64
is
&times;
to
only
of
rule
be
then
expanded
rule
squares
outsoitisomy.ie#witha--b?--hfmmm
SO,
in
the
the same
is
of
-
end
this
as
doing
ba Tba
rule
-
works
aca
b)
-
ba
=
the
t
because
b ca
-
b)
,
it's
which
-
the
-
*
CPE_T---RFECTSQUARESEXPANSION
general
example :
=
2
Cbt 3)
62
=
true
36
t
81
=
is
+ Zab
1- 2C3)
36
=
this
of
2
cat b)
rule :
because
-
.
CG
.
city
+
32
9
t
+372
2
81
=
:
+
(9)
=
variable example
b2
+
G)
rule
2)2=(4932+245112)+22
16yd t 1 by + 4
=
t
this is
the
same
as
doing
.
.
.
product rule
City 1-2) City + 2)
lay ✗ Ky) toy ✗2) 1-(2&times;49) 1- (2&times;2)
16yd + 8y t 8y + 4
=
=
=
=
16yd
t
1
by
4
t
prt}
oductruleisaiongerprocessandtaKesmh
SO
,
this
rule
simpler
way
applying
work
does
more time
it
is
a
much
doing catb) Catb) and
product rule , since the
of
the
because
FUR-tt-LREXPAN5-ON-h-lkfurt.tn
-
two
than
more
together
for these
→
first
in
(✗
example :
=
{
LIKE
brackets
+
are
→
5) Cx't
terms
each term
3&times;1-27
X
⇐
multiplied by
2x
+
5&times;2
simplified
15&times;+2 &lt;= 5
+
2nd
⇐
3+8&times;2-1
bracket
multiplied by
each term
17&times;+2
↳ SIMPLEST VERSION
in
2nd
bracket
✗
=
the
each term in
It 3&times;2
+
works
term in
multiplied by
brackets
of
set
each
still
is
CX.IT/-Cx.3x)tCX- 2)
=
being multiplied
distributive law
the
second
containing
expressions
terms
expansions
of
set
the
is
expansion
er
altnougntnevesnauabebtotaitevms.since.mn
{
2
terms
in
2nd
if
you
1st bracket
bracket
gives
simplify
the
and
us
=
3
terms in
2&times;3
expression
,
=
it
6
the
but
,
becomes
}
4
ternent
when
each
two
3
multiplying
contains
brackets
expansion
example :
2
Cx +
terms
first,
process
1) CX
brackets
,
you
because
it
simpler
-
3) (x
+
4)
together
expand
will
that
the
first
make the
cxt 1) Cx -33
=
=
=
=
(X
did
=
3✗
-
(✗2- 2x
(✗
.
3
=
X ) + CX
.
✗
✗
3
2)
✗
+
t
+
-
.
3) t u X)
.
-
✗
-
3)
t Cl
(x -2&times;3+(11--3)
+
(4&times;2) 1-(-2&times;4)
+
.
2&times;2
-
in
expand
12
FOIL ,
first
two
brackets
C- 3- 4)
C-3&times;-8&times;7
-
5- using
multiply these two
expressions
⇐ now , you
+
+
3)
-
CX +47
✗
3) (X + 4)
(-2&times;2+4&times;2)
.
←
⇐
connecting
like terms
-
12
SIMPLEST VERSION
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-
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but
if
the
expression
is
simplified
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-
b)
^
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↳
b)
is
2
find
to
a
@
=
*
=
as
+
of b
&gt;
a
t
3a2b
BBC.at b)
we
to
2a2b
+
3ab2
t
+
expand
I
I
we can
use
2
10
5
15
21
tells
term
20
35
us
that
bi
b3
Triangle pattern
O
=
=/
n=2
-
I
n
-
I
I
35
21
the
will
4
=
n
-
6
15
=3
n
-
5
10
+
ab
SIMPLIFIED
⇐
n
4
6
4
7
triangle
3
'
t
cat b)
-
I
expansion
n
n
l
3
6
1
each
can
further
Pascal's
-
l
I
}
b
binomial
a
I
1
we
method
2ab2
the
use
can
I
this
⇐ now
,
Cat
for
rule
pascal 's triangle:
*
?
the
t
↳ general
OR ,
contains
:( atb)
rule
squares
it
as
cat b)
→
perfect
binomial
a
terms
Zab t
+
positive integer !
a
general rule of
expand it first
cat b)
=
=
the
is
n
where
I
=
n=6
-
71
5
-
n
=
7
coefficients
be
expanded
of
*
also
,
have
→ / Ca5) t
*
↳
as
t
'
5a4b +
notice
!
in
*
↳
also
gets
wa3y2
that
one
n
.
5
10
10
a2b3
sum
always
the
term
,
larger
10
the
term
each
to
equal
5
I
+
that
see
notice
=
must
I
Sabit
of
=
exponent
while
each
+
the
the
5
,
of
'
t
b
exponents
which is n
a
without
exponent
of
b
term
really
.
gets
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binomials
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+
one
smaller
that
exponents
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expansion
of the
example , catb}
for
=
term
each
having
to
-
\$
crista
rule
rule:
general
q3
=
-
abt
b4
b
23-12/+118+112 -118+33
=
=
variable
-
}
(22-61-32)
(2+3)
example :
Cot
catb)
23
33
-
example
(4&times;-12)
:
41&times;13
=
-2*6*+23&times;1 -1/6*-23
-
64&times;3
=
C&Eacute;&yen;&Ntilde; -8&times;1-(-1%2)
-
23
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terms
thus
a
-
single
it
,
'
b
middle
leaving
only
expression
&gt;
do
the
in
,
will
of
save
multiplication
of
.
cancel
-
b?
time
out ,
Therefore,
to
just
expanding every
```