## CBSE Class 8 Maths Chapter 9 Notes Algebraic Expressions and Identities

### Algebraic Expressions and Identities Class 8 Notes Conceptual Facts

1. Algebraic Expression: A combination of numbers which includes literal number connected by the

symbols +, -, x and + is called an algebraic expression.

For example: 5x, 8x -3, 2x + 3y, \(\frac{3}{4}\)x^{2} 4xyz are some algebraic expressions.

Here. 5, 8, 3, 2. and 4 are constants and the literal numbers are x, y and z.

The different parts of the expression are called terms.

5x, 8x, 2x, 3y, \(\frac{3 x^{2}}{4}\) etc., are all the terms.

2. Coefficient: A coefficient is a multiplicative factor in some term of a polynomial. It is usually a number,

but may be only expression along.

For example in 7x^{2} – 3xy + y + 3. The first three terms respectively have coefficient 7, -3 and 3 is a

constant in given polynomial.

3. Monomial: The expression having only one term is called monomial.

For example: 3x, 8xy, 6×2, 11xyz, etc.

4. Binomial: The expression containing two terms is called binomial.

Forexample: 2x +y,x +y, 3xy-5z, \(\frac{1}{2}\) xy + 5, etc.

5. Trinomial: The expression containing three terms is called trinomial.

For example: x + 2y + 3, xy – z +\(\frac{1}{2}\) , \(\frac{1}{2}\) x^{2}+ 2x + 5, etc.

6. Polynomial: Algebraic expression containing one or more terms with non-zero coefficient is called a

polynomial.

For example: 2+3x, x+y+3z-5, \(\frac{1}{2}\) x^{2}+yz -5, etc.

7. Like and Unlike Terms: Algebraic expressions having same combination of literal numbers are called

like terms.

For example: 4xy, -5xy, –\(\frac{17}{3}\) xy, are like terms.

8. Algebraic expressions having different combinations of literal numbers are called unlike terms.

For example: (xy, yz, zx), (2x^{2}, – 5xy^{2}, 7xyz), (3, – 5x, 7yz) etc.

9. Degree of Algebraic Expression: Highest power of the variable of an algebraic expression is called its degree.

For example: Degree of 3x^{2} – 7x + 5 is 2.

Addition or Subtraction of two or more polynomials:

- Collect the like terms together.
- Find the sum or difference of the numerical coefficients of these terms.

For example:

(i) Add: 2x^{2}y^{3}, -5x^{2}y^{3} + \(\frac{11}{2}\)x^{2}y^{z
}Answer:

(ii) Subtract: (3x – 5) from (8x – 25)

Answer:

[Arrange the terms columnwise and change the sign of and add]

Multiplication Rule of Signs:

(+x) x (+y) = (+xy)

(+x) x (-y) = (-xy)

(-x) x (y) = (-xy)

(-x) x (-y) = (+xy)