## Algebra Formulas in Maths

Algebra is a branch of mathematics that deals with **algebraic expressions made up of variables and constants**. It has a vital role to play in every career option using a computer to calculator. **Algebra is taught to children from school to college (if opt for the engineering field) and competitive examinations like SSC, Banking, RRB, etc**. It is said that Algebra is the stepping stone to your success and a firm grasp of Algebraic expressions and formulae helps to excel in your career. In this article, we will provide you with a complete list of Algebra Formulas, Algebraic Expressions, Algebra Formula Charts, and related questions.

## Algebraic Expressions Formula

**Algebraic Expression** is defined as the mathematical expression made up of variables and constants, in addition to algebraic operations like multiplication, subtraction, addition, etc. There are **mainly three kinds of Algebraic Expression** as explained given below.

**Monomial Expression-**

This Algebraic Expression has only a single term like 2x, 6y, etc.

**Binomial Expression-**

This Algebraic Expression has two terms like 6xy+5, xy+ y², etc.

**Polynomial Expression-**

This Algebraic Expression has more than two terms with the non-negative integral exponents of a variable like 6x²+4x+7, 3y³+5y+15, etc.

## Basic Algebra Formulas

An algebraic expression or Equation is made when the vectors, numbers, letters, and matrices are combinedly used in Algebra Formulas. In a general view of the Algebraic Expression, the value of the number used in the equation is known but the value of the letter used is unknown. Hence Algebra Formulas are applied to find out the values of unknown quantities. **The Basic Algebra Formulas are mentioned below in the table**.

Basic Algebra Formula | |

1. | (a+b)² = a² + 2ab + b² |

2. | (a-b)² = a² – 2ab + b² |

3. | a² – b² = (a-b)(a+b) |

4. | a² + b² = (a-b)² +2ab |

5. | (a+b+c)² = a²+b²+c²+2ab+2ac+2bc |

6. | (a-b-c)² = a²+b²+c²-2ab-2ac+2bc |

7. | (a+b)³ = a³+ 3a²b + 3ab² + b³ |

8. | (a-b)³ = a³- b³ + 3ab² - 3a²b |

9. | a³-b³ = (a² + ab + b²)(a - b) |

10. | a³+b³ = (a² – ab + b²)(a + b) |

## Algebra Formula Chart

**Algebra** is a mathematical study that deals with geometry, number theory, and analysis. It has a vast reach to cover from solving elementary equations to the study of abstractions. The Algebra Formulas have always been an important topic for almost all competitive examinations. **The complete list of Algebra Formulas and Expressions is tabulated below.**

Algebra Formulas Chart | |

1. | a⁴ – b⁴ = (a² + b²) (a² – b²) |

2. | a⁵ – b⁵ = (a – b)(a⁴+ a³b + a²b² + ab³ + b⁴ ) |

3. | a⁵ + b⁵ = (a + b)(a⁴ – a³b + a²b²– ab³ + b⁴ ) |

4. | a³ + b³+ c³– 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca) |

5. | (a + b + c+...)² = a²+b²+c²+...+2(ab + bc+....) |

6. | If n is a natural number, a^n − b^n = (a−b)(a^(n−1) + a^(n−2) b+...+b^(n−2) a + b^(n−1)) |

7. | If n is even (n=2k), a^n + b^n = (a+b)(a^(n−1) − a^(n−2) b+...+b^(n−2) a − b^(n−1)) |

8. | If n is odd (n=2k+1), a^n + b^n = (a+b)(a^(n−1) − a^(n−2) b +...−b^(n−2) a + b^(n−1)) |

9. | (x+y+z)²=x²+y²+z²+2xy+2yz+2xz |

10. | (x+y−z)²=x²+y²+z²+2xy−2yz−2xz |

11. | (x−y+z)²=x²+y²+z²−2xy−2yz+2xz |

12. | (x−y−z)²=x²+y²+z²−2xy+2yz−2xz |

13. | x³+y³+z³−3xyz=(x+y+z)(x²+y²+z²−xy−yz−xz) |

14. | x²+y²=1/2[(x+y)²+(x−y)²] |

15. | (x+a)(x+b)(x+c)=x³+(a+b+c)x²+(ab+bc+ca)x+abc |

16. | x²+y²+z²−xy−yz−zx=1/2[(x−y)²+(y−z)²+(z−x)²] |

**Laws of Exponents-**

Some **basic laws of exponents are used** while calculating complex exponential expressions. Students do not need to expand the exponential terms while solving the exponential expressions and they can easily compute the greater exponential values.

- (a^m)(a^n)=a^(m+n)
- (ab)^m=a^m b^m
- (a^m)^n=a^(mn)

**Fractional Exponents-**

- a^0=1
- a^m / a^n = a^ (m−n)
- a^m = 1/a^(−m)
- a^(−m) = 1/a^m

## Algebra Formulas Related Questions

Some of the important questions related to Algebra are mentioned below. These questions will help you a lot for a better understanding of the Algebra concepts.

**Question 1: Find out the Algebraic Expression 8y+6 when y=3 **

**Solution:** Putting the value of y in the given expression we get,

8 (3)+6 = 30

**Question 2: A total 47 number of boys are there in a class. The number of boys is three more than four times the number of girls in that class. How many girls are present in the class?**

**Solution:** Let the number of girls in the class be y

According to the question, the expression to be

No. of Boys in the class = 3 + 4y = 47

4y = 44

So the number of girls in the class is y = (44/4) = 11

**Question 3: Find the value of y in (y-1)² = [4√(y-4)]²**

**Solution:** y²-2y+1 = 1Triangle6(y-4)

y²-2y+1 = 16y-64

y²-18y+65 = 0

(y-13) (y-5) = 0

Hence the value of y = 13 and y = 5