# Algebra

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## Basic formula for Algebra

1) (a + b)2 = a2 + b2 + 2ab

2) (a - b)2 = a2 + b2 - 2ab

3) (a + b)2 + (a - b)2 = 2(a2 + b2)

4) (a + b)2 - (a - b)2 = 4ab

5) (a2 - b2) = (a - b)(a + b)

6) (a + b)3 = a3 + b3 + 3ab(a + b)

7) (a - b)3 = a3 - b3 - 3ab(a - b)

8) (a3 + b3) = (a + b)(a2 - ab + b2)

9) (a3 - b3) = (a - b)(a2 + ab + b2)

10) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

11) (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
If a + b + c = 0 then a3 + b3 + c3 = 3abc

12) (a + b + c + d)2 = [a2 + b2 + c2 + d2 + 2a(b + c + d) + 2b(c + d) + 2cd]

### Linear Equation in one variable

General form of a linear equation in one variable is ax + b = 0, where a, b are real numbers and a ≠ 0.
Examples of linear equations in one variable: 2x + 5 = 0, 3x - 4 = 0

### Linear Equations in two variables

General form of a linear equation in two variable is ax + by = c where a, b, c are real numbers and a ≠ 0, b ≠ 0.
Examples of linear equations in two variables: 2x + 3y = - 5, 3x - 4y = 7
In order to solve a linear equation in 'n' variables we need atleast 'n' equations.