CBSE NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.4 (Ex. 9.4) Algebraic Expressions and Identities updated for CBSE academic session 2022-2023. Videos related to each question are given with PDF solutions free to use without any login. Exercise 9.4 of class 8 Maths is based on the product of two binomials. Here we will learn how to multiply two binomial terms using direct method and identities. All the questions of exercise 9.4 are given here with solution with simple method.

## Class 8 Maths Chapter 9 Exercise 9.4 Solution

 Class: 8 Mathematics Chapter: 9 Algebraic Expressions and Identities Exercise: 9.4 Solution in Hindi and English

### Class 8 Maths Chapter 9 Exercise 9.4 Solution in Videos

Class 8 Maths Chapter 9 Exercise 9.4 Solution
Class 8 Maths Chapter 9 Exercise 9.4 Explanation

#### IV. Multiplication of Two Polynomials

We may extend the above result for two polynomials, as shown below.

### Multiply: (i) (x³ – 3x² + x + 6) by (1 – 2x + 3x²)

x³ X (1 – 2x + 3x²) – 3x² X (1 – 2x + 3x²) + x X (1 – 2x + 3x²) + 6 X (1 – 2x + 3x²)
= x³ – 2x⁴ + 3x⁵ – 3x² + 6x³ – 9x⁴ + x – 2x² + 3x³ + 6 – 12x + 18x²
= 3x⁵ – 11x⁴ + 10x³ + 12x² – 11x + 6

##### Division of Algebraic Expressions

Rule:
If x is a variable and m, n are positive integers such that m > n then
Xᵐ/xⁿ = xᵐ⁻ⁿ

##### I. Division of a Monomial by a Monomial

Rule:
Quotient of two monomials = (quotient of their numerical coefficients) x (quotient of their variables)

### Divide: (i) 8x² y³ by -2xy (ii) -15x³ yz³ by -5xyz²

We have:
(i) (8x² y³)/-2xy = (8/-2) (x²⁻¹ y³⁻¹
= -4xy²
(ii) (-15x³ yz³)/-5xyz² = (-15/-5) (x³⁻¹ y1-1 z³⁻²)
= 3x² z

##### II. Division of a Polynomial by a Monomial

Rule
For dividing a polynomial by a monomial, divide each term of the polynomial by the monomial.

### Divide: (i) 6×5 + 18x⁴ -3x² by 3x² (ii) 20x³y + 12x²y² – 10xy by 2xy

(i) (6x⁵ + 18x⁴ -3x²) /3x²
= 6x⁵ /3x² + 18x⁴ /3x² – 3x²/3x²
= 2x⁵⁻² + 6x⁴⁻² – 1x²⁻²
= 2x³ + 6x² – 1
(ii) (20x³ y + 12x² y² – 10xy) /2xy
= (20x³ y)/ 2xy + (12x² y²)/ 2xy – (10xy) /2xy
= 10x³⁻¹ y¹⁻¹+ 6x²⁻¹ y²⁻¹ – 5x¹⁻¹ y¹⁻¹
= 10x² + 6xy – 5

### How do you solve polynomials by dividing?

How do you solve polynomials by dividing?
Divide the first term of the numerator by the first term of the denominator, and put that in the answer.
Multiply the denominator by that answer, put that below the numerator.
Subtract to create a new polynomial.

### What are two ways to divide polynomials?

There are two ways to calculate a division of polynomials. One is long division and a second method is called synthetic division. Synthetic division can be used when the polynomial divisor such as x-2 has the highest power of x as 1 and the coefficient of x is also 1.

### Why do we need polynomials in life?

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. … Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Engineers use polynomials to graph the curves of roller coasters and bridges.      