The document Points to Remember - Algebraic Expressions and Identities Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by Full Circle.

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**Points to Remember**** **

- Expressions containing one, two or three terms are called monomial, binomial and trinomial respectively.
- Any expression having one or more terms is called a polynomial.
- Any monomial multiplied by a monomial gives a monomial.
- The numerical factor of a term is called its coefficient.
- An identity is an equality, which is true for all values of the variables in the equality.
- The standard identities are:

(a + b)^{2}= a^{2}+ 2ab + b^{2}…(i)

(a – b)^{2}= a^{2}– 2ab + b^{2}…(ii)

(a + b)(a – b) = a^{2}– b^{2}…(iii)

(x + a)(x + b) = x^{2}+ (a + b)x + ab …(iv)

**We Know That**

Algebraic expressions are formed from the variables and constants. A variable can take any value. The value of an expression changes with the value chosen for the variables it contains.

A number line has countless points. A variable can take position on the number line.**Like and Unlike Terms**

The terms having the same literal factors are called like (or similar) terms, otherwise they are called unlike (or dissimilar) terms.**Addition and Subtraction of Algebraic Expressions****Example 1. ****Add: 9xy – 3yz + 2zx; 2xz + 9xy – 4y and –2xz + 5x + 3xy.****Solution:** We write the expressions in separate rows, keeping like terms in the same column:

Note:I. In the above example, –4y and 5x are carried over as they are, because they have no like terms.

II. xz is same as zx.

**Example 2.** Subtract 6x^{2} – 5y^{2} + 7y – 4 from 8x^{2} – 5xy + 9y^{2} + 6x – 4y**Solution: **We know that subtraction of a number is the same as addition of its additive inverse.

We have**Example 3. Which of the following is a binomial?a. 8*a+ab. 7a**d. 11a

a) will give 8a+a=9a which is monomial.

b) is a trinomial

c) will give 24abc, which is a monomial

d) will give 11a^{2}+11b^{2}, which is a binomial**Example 4. Identify the variable, exponent, and coefficient in the given term of 3/5 k8Solution: **Here the variable is k, the exponent is 8 and coefficient is 3/5.

Solution:

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