Important Formulas: We Distribute, Yet Things Multiply | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Algebraic expression is the expression having constants and variable. It can have multiple variable and multiple power of the variable
Example:

• 11x
• 2y – 3
• 2x + y

Some Important points on Algebraic expressions

1. Terms
Terms are added to form expressions

2. Factors
Terms themselves can be formed as the product of factors

3. Coefficient

The numerical factor of a term is called its numerical coefficient or simply coefficient.

4. Monomial
Algebraic expression having one terms is called monomials
Example: 3x 

5. Binomial
Algebraic expression having two terms is called Binomial
Example: 3x+y

6. Trinomial

Algebraic expression having three terms is called Trinomial
Example: 3x+y+z 

7. Polynomial: An expression containing, one or more terms with non-zero coefficient (with variables having non negative exponents) is called a polynomial.

8. Like Terms: When the variable part of the terms is same, they are called like terms

9. Unlike Terms: When the variable part of the terms is not same, they are called unlike terms.

Operation on Algebraic Expressions

1. Addition

(a) We write each expression to be added in a separate row. While doing so we write like terms one below the other
Or
We add the expression together on the same line and arrange the like term together
Example : Add (2x + 3) and (4x + 5)
(2x+3 ) +(4x + 5)
(b) Add the like terms
2x+ 4x= 6x
3+5= 8

(c) Write the Final algebraic expression
6x+8

2. Subtraction

(a) We write each expression to be subtracted in a separate row. While doing so we write like terms one below the other   and then we change the sign of the expression which is to be subtracted i.e. + becomes – and – becomes +
Or
We subtract the expression together on the same line, change the sign of all the term which is to be subtracted and then arrange the like term together
Example : (5y+10)- (3y+7)
5y+10-3y-7

(b) Subtract the like terms
5y-3y=2y
10-7=3

(c) Write the Final algebraic expression
2y+3

3. Multiplication

(a) We have to use distributive law and distribute each term of the first polynomial to every term of the second polynomial.
Example : Multiply (x + 2) and (x + 3)
(x+2) * (x+3)
(b) when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents
x.x + x.3 + 2.x + 2.3
x²+ 3x+ 2x+6
(c) Also as we already know ++ equals =, +- or -+ equals - and -- equals +
(d) group like terms
x²+5x+6

Standard Identities

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² – 2ab + b²
• a² – b² = (a + b) (a - b)
• (x + a) (x + b) = x² + (a + b)x + ab
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca