Algebra Formulas: List Of Algebraic Expressions & Formulas

Algebra Formulas: Mathematics typically covers a vast area and is one of the important fields of study. As students approach higher classes, they get introduced to Algebra. When the fixed and dynamic components come hand in hand to determine a specific situation, Algebra comes into play. Sometimes Algebraic Expressions in Maths may get too tough to handle and that is where Embibe comes to your rescue. In this article, we will provide you with the list of Algebraic Expressions in Maths, their definition, and examples. Also, know the basic Algebraic Formulas and Expression.

List Of Algebraic Expressions In Maths

Algebra is represented as the study of unknown quantities. These become important for the students studying in Class 6 till the higher classes. This article on Algebra Formulas and Expression will tell you about the following topics.

1. Algebraic Identities
2. Laws of Exponent
3. Quadratic Equations
4. List of important formulas

   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 the order 1. It is depicted in the form of ax + b = 0, where x is represented as the variable.
   • 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.
   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 × … 9 more 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 Formulas: 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 the equation ax2 + bx + c = 0 (where a ≠ 0) can be given as:
   −b±b2−4ac√2a$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
   1. Δ = b2 − 4ac is also known as discriminant.
   2. For roots;
      1. Δ > 0 happens when the roots are real and distinct
      2. For real and coincident roots, Δ = 0
      3. Δ < 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

   Generic Algebra Formulas

   The general 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 + ….)

   List Of Important Algebra Formulas

   Here is an important list of 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]