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Important Formulas
Problems on Numbers
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General Aptitude
Problems on Numbers
Important Formulas
1.
Some Basic Formulae:
i.
(
a
+
b
)(
a
-
b
) = (
a
2
-
b
2
)
ii.
(
a
+
b
)
2
= (
a
2
+
b
2
+ 2
ab
)
iii.
(
a
-
b
)
2
= (
a
2
+
b
2
- 2
ab
)
iv.
(
a
+
b
+
c
)
2
=
a
2
+
b
2
+
c
2
+ 2(
ab
+
bc
+
ca
)
v.
(
a
3
+
b
3
) = (
a
+
b
)(
a
2
-
ab
+
b
2
)
vi.
(
a
3
-
b
3
) = (
a
-
b
)(
a
2
+
ab
+
b
2
)
vii.
(
a
3
+
b
3
+
c
3
- 3
abc
) = (
a
+
b
+
c
)(
a
2
+
b
2
+
c
2
-
ab
-
bc
-
ac
)
viii.
When
a
+
b
+
c
= 0, then
a
3
+
b
3
+
c
3
= 3
abc
.
