# NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.3

CBSE NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.3 (Ex. 9.3) Algebraic Expressions and Identities in Hindi and English Medium updated for academic session 2021-2022. The entire content on Tiwari Academy is free to use without any formal registration.

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## Class 8 Maths Chapter 9 Exercise 9.3 Solution

 Class: 8 Mathematics Chapter: 9 Algebraic Expressions and Identities Exercise: 9.3 Hindi and English Medium Solution

### Class 8 Maths Chapter 9 Exercise 9.3 Solution in Videos

Class 8 Maths Chapter 9 Exercise 9.3 Solution
Class 8 Maths Chapter 9 Exercise 9.3 Explanation

#### Multiplication of Algebraic Expressions

Before taking up the product of an algebraic expressions, let us look at two simple rules.
(i) The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
(ii) If x is a variable and m, n are positive integers, then (x3 X x5) = x(3 + 5) = x8
Thus, (x6 X x4) = x(6 + 4) = x10 , etc.

##### I. Multiplication of Two Monomials

Rule: Product of two monomials = (product of their numerical coefficients) x (product of their variable parts)

##### Find the product of: (i) 6xy and -3×2 y3 (ii) 7ab2, -4a2 b and -5abc

We have:
(i) (6xy) x (-3x² y³) = {6 x (-3)} x {xy X x² y³}
= -18 {x³ y⁴} = -18x³ y4
(ii) (7ab²) x (–4a² b) x {–5abc} = {7 x (–4) x (–5) x {ab² x a² b x abc}
140a⁴ b⁴ c = 140a⁴ b⁴ c.

##### II. Multiplication of A Polynomial by a Monomial

Rule
Multiply each term of the polynomial by the monomial, using the distributive law:
a x (b + c) = a x b + a x c

##### Find each of the following products: (i) 5a² b² (3a² – 4ab + 6b²)

We have:
(i) 5a² b² (3a² – 4ab + 6b²) = (5a² b²) x (3a) + (5a² b²) x (–4ab) + (5a² b²) x (6b²)
15a³b² – 20a³b³ + 30a²b⁴

##### III. Multiplication of Two Binomials

Suppose (a + b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.
(a+ b) x (c + d) = a x (c + d) + b x (c + d)
= (a x c + a x d) + (b x c + b x d) = ac + ad + bc +bd.
This method is known as the horizontal method.

##### Multiply (3x + 5y) and (5x – 7y).

Multiply (3x + 5y) and (5x – 7y).
We have:
(3x + 5y) X (5x – 7y) = 3x X (5x – 7y) + 5y X (5x – 7y) = (3x X 5x – 3x X 7y) + (5y X 5x – 5y X 7y)
= (15x² – 21xy) + (25xy – 35y²) = 15x² + 4xy – 35y²

##### How do you solve polynomial multiplication?

To multiply two polynomials: multiply each term in one polynomial by each term in the other polynomial. add those answers together, and simplify if needed.

##### What are the properties of polynomial multiplication?

distributive property
When multiplying polynomials, the distributive property allows us to multiply each term of the first polynomial by each term of the second. We then add the products together and combine like terms to simplify.

##### Why is multiplying polynomials important?

Multiplying polynomials involves applying the rules of exponents and the distributive property to simplify the product. Polynomial multiplication can be useful in modeling real world situations. Understanding polynomial products is an important step in learning to solve algebraic equations involving polynomials.      