# Algebra Formula

Updated: 24 Aug 2023

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Mathematics consists of endless branches. Each branch has many formulas called math formulas used to solve mathematical problems. Math formula helps to solve the question quickly. Mathematical formulas are used in arithmetic, percentages, algebra, geometry, etc. This article is about basic algebra formulas or algebraic formulas.

## Define Algebra Formula

An algebra formula is a mathematical expression that involves variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These formulas represent relationships between quantities and can be manipulated to solve equations, analyze patterns, etc. Algebraic formulas often describe general rules or patterns that can be applied to various situations.

## List of Algebra Formulas

1. (a+b)^2=a^2+b^2+2 a b
2. (a-b)^2=a^2+b^2-2 a b
3. \left(x+\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}+2(x)\left(\frac{1}{x}\right)
4. \left(x-\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}-2(x)\left(\frac{1}{x}\right)
5. \left(x+\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}+2
6. \left(x-\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}-2
7. (a+b)^2+(a-b)^2=2\left(a^2+b^2\right)
8. (a+b)^2-(a-b)^2=4 a b
9. (a+b)(a-b)=a^2-b^2
10. (a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)
11. (a+b)^3=a^3+b^3+3 a b(a+b)
12. (a-b)^3=a^3-b^3-3 a b(a-b)
13. \left(x+\frac{1}{x}\right)^3=x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right)
14. \left(x-\frac{1}{x}\right)^3=x^3-\frac{1}{x^3}-3\left(x-\frac{1}{x}\right)
15. a^3+b^3=(a+b)\left(a^2-a b+b^2\right)
16. a^3-b^3=(a-b)\left(a^2+a b+b^2\right)
17. x^3+\frac{1}{x^3}=\left(x+\frac{1}{x}\right)\left(x^2-(x)\left(\frac{1}{x}\right)+\frac{1}{x^2}\right)
18. x^3-\frac{1}{x^3}=\left(x-\frac{1}{x}\right)\left(x^2+(x)\left(\frac{1}{x}\right)+\frac{1}{x^2}\right)
19. x^3+\frac{1}{x^3}=\left(x+\frac{1}{x}\right)\left(x^2+\frac{1}{x^2}-1\right)
20. x^3-\frac{1}{x^3}=\left(x-\frac{1}{x} \right) \left(x^2+\frac{1}{x^2}+1\right)
21. a^2-b^2=(a+b)(a-b)
22. (a+b)^2-c^2=(a+b+c)(c+b-c)

## Algebra Formulas – MCQs

1. (a+b)^2=

a^2+b^2+2 a b

2. (a-b)^2=

a^2+b^2-2 a b

3. \left(x+\frac{1}{x}\right)^2=

x^2+\frac{1}{x^2}+2(x)\left(\frac{1}{x}\right)

4. \left(x-\frac{1}{x}\right)^2=

x^2+\frac{1}{x^2}-2(x)\left(\frac{1}{x}\right)

5. \left(x+\frac{1}{x}\right)^2=

x^2+\frac{1}{x^2}+2

6. \left(x-\frac{1}{x}\right)^2=

x^2+\frac{1}{x^2}-2

7. (a+b)^2+(a-b)^2=

2\left(a^2+b^2\right)

8. (a+b)^2-(a-b)^2=

4 a b

9. (a+b)(a-b)=

a^2-b^2

10. (a+b+c)^2=

a^2+b^2+c^2+2(a b+b c+c a)

11. (a+b)^3=

a^3+b^3+3 a b(a+b)

12. (a-b)^3=

a^3-b^3-3 a b(a-b)

13. \left(x+\frac{1}{x}\right)^3=

x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right)

14. \left(x-\frac{1}{x}\right)^3=

x^3-\frac{1}{x^3}-3\left(x-\frac{1}{x}\right)

15. a^3+b^3=

(a+b)\left(a^2-a b+b^2\right)

16. a^3-b^3=

(a-b)\left(a^2+a b+b^2\right)

17. x^3+\frac{1}{x^3}=

\left(x+\frac{1}{x}\right)\left(x^2-(x)\left(\frac{1}{x}\right)+\frac{1}{x^2}\right)

18. x^3-\frac{1}{x^3}=

\left(x-\frac{1}{x}\right)\left(x^2+(x)\left(\frac{1}{x}\right)+\frac{1}{x^2}\right)

19. x^3+\frac{1}{x^3}=

\left(x+\frac{1}{x}\right)\left(x^2+\frac{1}{x^2}-1\right)

20. x^3-\frac{1}{x^3}=

\left(x-\frac{1}{x}\right)\left(x^2+\frac{1}{x^2}+1\right)

21. a^2+2 a b+b^2=

(a+b)^2

22. a^2-2 a b+b^2=

(a-b)^2

23) x^2+2(x)\left(\frac{1}{x}\right)+\frac{1}{x^2}=

\left(x+\frac{1}{x}\right)^2

24) x^2-2(x)\left(\frac{1}{x}\right)+\frac{1}{x^2}=

\left(x-\frac{1}{x}\right)^2

25) x^2+2+\frac{1}{x^2}=

\left(x+\frac{1}{x}\right)^2

26) x^2-2+\frac{1}{x^2}=

\left(x-\frac{1}{x}\right)^2

27) a^2-b^2=

(a+b)(a-b)

28) (a+b)^2-c^2=

(a+b+c)(c+b-c)

29) (a+b)^3=

a^3+3 a^2 b+3 a b^2+b^3

30) (a-b)^3=

a^3-3 a^2 b+3 a b^2-b^3

31) (a+b)\left(a^2-a b+b^2\right)=

a^3+b^3

32) (a-b)\left(a^2+a b+b^2\right)=