ALGEBRAIC FORMULA

                   

List Of Important Algebra Formulas

Here is a complete list of all the important algebra formulas:

1. (a + b)2 = a2 + 2ab + b2
2. (a – b)2 = a2 – 2ab + b2
3. (a + b) (a – b) = a2 – b2
4. (x + a) (x + b) = x2 + (a + b) x + ab
5. (x + a) (x – b) = x2 + (a – b) x – ab
6. (x – a) (x + b) = x2 + (b – a) x – ab
7. (x – a) (x – b) = x2 – (a + b) x + ab
8. (a + b)3 = a3 + b3 + 3ab (a + b)
9. (a – b)3 = a3 – b3 – 3ab (a – b)
10. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
11. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
12. (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
13. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
14. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
15. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
16. x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
17. x2 + y2 = 12$\frac{1}{2}$ [(x + y)2 + (x – y)2]
18. (x + a) (x + b) (x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
19. x3 + y3 = (x + y) (x2 – xy + y2)
20. x3 – y3 = (x – y) (x2 + xy + y2)
21. x2 + y2 + z2 – xy – yz – zx = 12$\frac{1}{2}$ [(x – y)2 + (y – z)2 + (z – x)2]                     Algebra Formulas: Important Algebraic Identities

Algebraic identities comprise various equality equations consisting of different variables.

• a) Linear Equations in One Variable: A linear equation in one variable has the maximum of one variable present in order 1. It is depicted in the form of ax + b = 0, where x is represented as the variable.
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• b) Linear Equations in Two Variables: A linear equation in two variables consists of the utmost two variables present in order 2. The equation is depicted in the form: ax2 + bx + c = 0. The two variables are quite important because your course book has a lot of questions based on it. So, you need to stay focused on important algebra formulas to find the solution.

Some basic identities to note are:

1. The combination of literal numbers obeys every basic rule of addition, subtraction, multiplication and division.
2. x × y = xy; such as 5 × a = 5a = a × 5.
3. a × a × a × … 12 times = a12
4. If a number is x8, then x is the base and 8 is the exponent.
5. A constant is a symbol with a fixed numerical value.

Algebra Formula: Laws Of Exponent

Exponents are the powers or the degrees in any mathematical expression. Here are some laws of exponents important in learning algebra formulas (given below):

1. a0 = 1
2. a-m = 1/am
3. (am)n = amn
4. am / an = am-n
5. am x bm = (ab)m
6. am / bm = (a/b)m
7. (a/b)-m = (b/a)m
8. (1)n = 1 for infinite values of n.

Algebra Formulas: Quadratic Equations

Quadratic equations are simply the linear equations in two variables. These are quite important when it comes to solving mathematical questions.

The roots of a quadratic equation ax2 + bx + c = 0 (where a ≠ 0) can be given as:

−b±b2−4ac√2a$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Some important points about the equation as a part of important algebra formulas are given below:

1. D = b2 − 4ac is also known as the discriminant of quadratic equation.
2. For roots;
   • (i) D> 0 happens when the roots are real and distinct
   • (ii) For real and coincident roots, D = 0
   • (iii) D< 0 happens in the case when the roots are non-real
3. If α and β are the two roots of the equation ax2 + bx + c then,
   α + β = (-b / a) and α × β = (c / a).
4. If the roots of a quadratic equation are α and β, the equation will be
   (x − α)(x − β) = 0.

Important Algebra Formulas

The general algebra formulas can be given as:

1. n is a natural number: an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
2. If n is even: (n = 2k), an + bn = (a – b)(an-1 + an-2b +…+ bn-2a + bn-1)
3. n is odd: (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1)
4. General square Formula: (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc+...)

• =an+nan−1b+n(n−1)2!an−2b2+n(n−1)(n−2)3!an−3b3+….+bn,wher