Maths
Algebra
MORE ON ALGEBRA...
Addition/Subtraction Identities
Multiplication/Division Identities
Polynomial Identities
|
Powers - Identities
Logarithms - Identities
|
Surds - Identities
Addition/Subtraction Identities
a
+
0
=
a
a
+
(
-
a
)
=
0
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
a
+
b
=
b
+
a
a
-
b
=
a
+
(
-
b
)
Multiplication/Division Identities
a
×
1
=
a
a
×
(
1
a
)
=
1
a
×
0
=
0
(
a
×
b
)
×
c
=
a
×
(
b
×
c
)
=
a
×
b
×
c
a
×
b
=
b
×
c
a
×
(
b
+
c
)
=
(
a
×
b
)
+
(
a
×
c
)
=
ab
+
ac
a
b
=
a
×
(
1
b
)
Polynomial Identities
(
a
+
b
)
2
=
a
2
+
2
ab
+
b
2
(
a
+
b
)
(
c
+
d
)
=
ac
+
ad
+
bc
+
bd
(
a
2
-
b
2
)
=
(
a
+
b
)
(
a
-
b
)
(
a
3
+
b
3
)
=
(
a
+
b
)
(
a
2
-
ab
+
b
2
)
(
a
3
-
b
3
)
=
(
a
-
b
)
(
a
2
+
ab
+
b
2
)
x
2
+
x
(
a
+
b
)
+
ab
=
(
x
+
a
)
(
x
+
b
)
When
ax
2
+
bx
+
c
=
0
(
Quardratic
formula
)
:
x
=
-
b
±
b
2
-
4
ac
2
a
Power - Identities
x
0
=
1
x
1
=
x
x
a
x
b
=
x
a
+
b
x
a
y
a
=
(
xy
)
a
(
x
a
)
b
=
x
(
ab
)
x
(
a
b
)
=
x
a
b
x
1
2
=
x
x
-
a
=
1
x
a
x
(
a
-
b
)
=
x
a
x
b
Logarithms - Identities
y
=
log
b
(
x
)
iff
x
=
b
y
log
b
(
1
)
=
0
log
b
(
b
)
=
1
log
b
(
xy
)
=
log
b
(
x
)
+
log
b
(
y
)
log
b
(
x
y
)
=
log
b
(
x
)
-
log
b
(
y
)
log
b
(
x
n
)
=
n
log
b
(
x
)
log
b
(
x
)
=
log
b
(
c
)
log
c
(
x
)
=
log
c
(
x
)
log
c
(
b
)
Surds - Identities
a
b
×
a
b
=
a
c
b
d
a
b
c
d
=
a
c
b
d
,
(
c
,
d
&neq;
0
)
a
b
+
c
b
=
(
a
+
c
)
b
a
b
-
c
b
=
(
a
-
c
)
b
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