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Algebra Formulas
1.
(a+b)
2
= ?
a
2
+b
2
+2ab
a
2
-b
2
+2ab
a
2
+b
2
+4ab
a
2
+b
2
-2ab
2.
(a-b)
2
=
a
2
+b
2
-2ab
a
2
+b
2
+2ab
a
2
+b
2
-ab
a
2
+b
2
-4ab
3.
(a+b)
2
+ (a-b)
2
=
2(a
2
+ 2b
2
)
2(a
2
- b
2
)
4(a
2
+ b
2
)
2(a
2
+ b
2
)
4.
(a + b)
2
- (a - b)
2
=
ab
4ab
-4ab
2ab
5.
(a+b+c)
2
=
a
2
+b
2
+2c
2
-2ab+2bc+2ca
a
2
+b
2
+c
2
+2ab+2bc-2ca
a
2
+b
2
+c
2
+2ab+2bc+2ca
a
2
+b
2
+c
2
+2ab+2bc+2ca
6.
(a+b)(a-b) =
4ab
a
2
+ b
2
a
2
- b
2
a
2
- b
4
7.
(a+b)
3
=
a
3
+b
3
+3ab(a-b)
a
3
+b
3
+3ab(a+b)
a
3
+b
3
+3ab
a
3
+b
3
+3(a+b)
8.
(a-b)
3
=
a
3
-b
3
+3ab
a
3
-b
3
-3ab(a+b)
a
3
-b
3
-3ab
a
3
-b
3
-3(a+b)
9.
a
2
+b
3
=
(a+b)(a
2
+b
2
-ab)
(a+b)(a
2
+b
2
-ab)(a+b)
(a+b)(a
2
+b
2
-2ab)
(a-b)(a
2
+b
2
-ab)
10.
a
3
-b
3
=
(a-b)(a
2
+ab+b
2
)
(a-b)(a
2
+ab+b
2
)
(a-b)(a
2
+ab+2b
2
)
(a-b)(a
2
+2ab+b
2
)
11.
a
3
+b
3
+c
3
-3abc =
(a+b+c)(a
2
+b
2
+c
2
-ab-bc-ca)
(a+b+c)(a
2
+b
2
+c
2
-ab-bc+ca)
(a+b+c)(a
2
-b
2
+c
2
-ab-bc-ca)
(a+b-c)(a
2
+b
2
+c
2
-ab-bc-ca)
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