This GSEB Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities covers all the important topics and concepts as mentioned in the chapter.

## Algebraic Expressions and Identities Class 8 GSEB Notes

→ Algebraic expressions are formed from variables and constants.

→ Constant is a symbol which has a fixed numerical value, such as -5, 7, etc.

→ A variable / literal is a symbol which does not have a fixed numerical value. In general, we use alphabets to represent variables.

→ In an algebraic expression, one or more signs separates it into several parts. Each part along with its sign is known as a term.

→ A polynomial with a single term is called a monomial.

e.g. 5x, -8y, 47, -105

→ A polynomial with two terms is called a binomial.

e.g. 3x + 2, – 12x + 1, 6-x, -7x-2y

→ A polynomial with three terms is called a trinomial.

e.g. 2x^{2} – 3x + 1, 8 – 4x^{3} + 9x^{2},

16x^{2} + 40xy + 25y^{2}

→ An expression containing one or more terms with non-zero coefficient is called a polynomial.

→ The terms which have the same variables with the same powers are called like terms, e.g. -5x^{2} and 7x^{2}; 6xy^{2}z and -8xy^{2}z

→ The terms which do not have the same variable are called unlike terms.

e.g. 3x and 5y; – 4×2 and -3xy; – 7x and 2y^{2}

→ Product of a monomial and a monomial: For the product of two monomials, their respective coefficients and their respective powers of the variables are multiplied.

→The product of two monomials is always a monomial.

→ The product of a monomial and a binomial:

We have learned the distribution of multiplication over addition, x × (y + z) = (x × y) + (x × z) = xy + xz

→ The distributive property is used as below: 2x × (3a + 5b) = (2x × 3a) + (2x × 5b)

= 6xa + 10xb

Thus, using the distributive property, the product given on the left side is expressed as the addition on the right side. This process is called expansion.

→ Identity: An equality which holds true for any value of the variables in it, is called an identity.

→ Identities:

- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b) (a – b) = a
^{2}– b^{2} - (x + a) (x + b) = x
^{2}+ (a + b)x + ab