Can I get all the algebra formula in one sheet? So, here is the answer Yes, you can get all the formula to solve the algebra problems. Basics of Mathematics include study of whole numbers, integers and natural numbers also we start learning about the functions like addition, subtraction, multiplication and division, BODMAS and many other formulas.

We are already aware of it that Algebra in Maths is a substitute letter for numbers.

Let’s focus on algebra formula and get started with it.

The general formulas used to solve any algebraic expression or equation are:

Algebra Identities or Algebra Formula

  • Identities 
(a+b) ^2= a^2+b^2+2(ab)
(a-b) ^2= a^2+b^2-2(ab)
a^2-b^2=(a+b) (a-b)
a^2+b^2=(a-b)^2+ 2ab
(a+b) ^3= a^3+b^3+3ba(a+b)
(a-b) ^3= a^3-b^3-3ba(a-b)
a^3+b^3=(a+b) (a^2+b^2-ab)
a^3-b^3=(a-b) (a^2+b^2+ab)
(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca
(a-b+c)^2=a^2+b^2+c^2-2ab-2bc+2ca
(a+b-c)^2=a^2+b^2+c^2+2ab-2bc-2ca
(a-b-c)^2=a^2+b^2+c^2-2ab+2bc-2ca
(a – b)^4 = a^4+ b^4 – 4a^3b + 6a^2b^2 – 4ab^3
(a + b)^4 = a^4 + b^4+ 4a^3b + 6a^2b^2 + 4ab^3
a^4 – b^4 = (a + b)(a^2 + b^2)(a – b)
a^5 – b^5 = (a – b)(a^4 + b^4+ a^3b + a^2b^2 + ab^3)
a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2+ab-bc-ca)
a^2+b^2+c^2-ab-bc-ca=\frac{1}{2}[(a-b)^2+(b-c)^2+(c-a)^2]
a^2+b^2 =\frac{1}{2}[(a+b)^2+(a-b)^2]

If n is a natural number then
a^n – b^n = (a – b)(a^{n-1} + ba^{n-2}+…+ ab^{n-2} + b^{n-1}) If n is even then
(n = 2k), a^n + b^n = (a + b)(a^{n-1} – a^{n-2}b +…+ ab^{n-2} – b^{n-1}) If n is odd then
(n = 2k + 1), a^n + b^n = (a + b)(a^{n-1} – a^{n-2}b +a^{n-3}b^2…- ab^{n-2} + b^{n-1})

  • Fraction exponent

Here, x^0=1 \frac {x^m}{x^n}=x^{m-n} x^{-m}=\frac{1}{x^m}

  • Law exponents
(x^m)(x^n) = x^{m+n} (xy)m = x^my^m (x^m)^n = x^{mn}
  •  Root of Quadratic equation

Given quadratic equation is ax^2+bx+c=0 where a±0
x=\frac{-b±\sqrt{b^2-4ac}}{2a} where,
D= b^2-4ac is the discriminant
D > 0, For real and distinct roots
D= 0, For real and coincident roots
D< 0, For non-real roots

Example of Algebra formula

Problem 1: Solve 4^2-2^2 using Algebra formula
Solution:
We have 4^2-2^2 Using the identity or above formula
a^2-b^2=(a+b) (a-b) here, a=4 and b=2
4^2-2^2=(4+2)(4-2) [Using BODMAS] =(6)(2)
=12
Hence, after solving the above equation the result is 12.

Problem 2: Solve (9+6)^2 using Algebra formula.
Solution:
We have (9+6)^2 Using the identity or above formula
(a+b)^2=a^2+b^2+2ab here, a=9 and b=6
(9+6)^2=9^2+6^2+2(9)(6) [Using BODMAS] =81+36+108
=225
Hence, after solving the above equation the result is 225.

Also, check out our Blogging for algebraic expression and algebra equations for more information on Algebraic expressions and Algebra in Maths to learn the basics of algebra to improving your knowledge to solve any problem easily. Do comment and let us know your opinion on it.

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