Algebra Formulas for class 12

Algebra Formula Class 12

What is algebra in Mathematics?

• Algebra is one of the branches of Mathematics which deals with variables and numbers.

• In Mathematics, algebra is one of the most important topics in which general symbols and letters represent quantities and numbers in equations and formulae.

•  Elementary algebra is the more basic parts of Algebra and more abstract parts are known as modern algebra or abstract algebra. 

• It is very important as it covers everything from elementary equation solving to the study of abstractions such as rings, groups, and fields.

What is an algebraic expression in Mathematics?

• An algebraic expression is a combination of constants and variables that are connected by addition, subtraction, multiplication, and division signs.

• Various parts of an algebraic expression that are separated by the signs of addition (+) or subtraction (-) are known as terms of the algebraic expression.

• An algebraic expression can be defined as a sum, difference, product, or quotient of constants and variables.

• Let us take an example,

 2x + 4 

The above expression is known as an algebraic expression where the value 

of x may vary, as x is a variable, and 4 is a constant. 2x and 4 are the terms of an algebraic expression that are separated by an addition (+) sign. Anything (a,b, c…….z) can be written in place of x as they all are variables.

Methods to verify algebraic identities:

1. Using the Substitution Method.

• Substitution generally means putting numbers or values in the place of variables or letters.

• In the substitution method, an arithmetic operation is performed by substituting the values for the variables.

• For example, when we have x-2=4

When we substitute x= 6, 

On the Right- hand side,

4

On the left-hand-side,

x-2 = 6-2 = 3

Here, Right-hand side = Left-hand side which means (x-2) is an identity.

Suppose, (a+3) (a-3) = (a2-9) 

Substituting a= 1

On the Right- hand side,

(a2-9) = (1-9) = -8

On the Left- hand side,

(a+3) (a-3) = (1+3) (1-3) = (4) (-2) = -8

Here, Right-hand side = Left-hand side which means that (a+3) (a-3) is an identity.

2. Using Activity Method.

• In this method, the algebraic identity is verified geometrically by taking different values of x and y.

• In the activity method, the identities are verified by cutting and pasting paper.

• To verify identity using this method, you need to have a basic knowledge of Geometry.

Standard identities in Mathematics you need to know!

List of Algebra Formulas Class 12:

Here is the list of Algebra Formula for class 12 that will help students to guide them in their study of algebra. Basic formulas of Algebra:

1. Formulas for powers-

2. Law of Exponents – 

3. Polynomial formulas-

Vector Algebra is included in the Class 12 mathematics syllabus. It generally deals with vectors – things that have both directions and magnitudes. Learning vector algebra will help you in handling geometric transformations and it also is very important in understanding Linear Algebra. Vectors hold great importance in both Physics and Mathematics.

12th Algebra Formulas

12th Algebra Formulas are of foremost importance at every level of competitive exams. You should memorize these formulas to crack all the Math competitive exams.

The main objective of solving the algebraic equation is to find the unknown variables in the expression.

Fun facts: 

Questions to be solved:

Question 1)Expand the following.

                                 (a + 2)(a-2)

Solution)  (a + 2) (a- 2)

Let’s multiply the given expression,

= We can simplify the question by using the formula, a2 - b2

= (a)2 – (2)2

= a2 – 4