CBSE NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.4 Algebraic Expressions and Identities in Hindi and English Medium updated for new session 2023-24. Get here the revised solutions of ex. 8.4 class 8th math based on new NCERT books for CBSE 2023-24.
|Chapter: 8||Exercise: 8.4|
|Topic Name:||Algebraic Expressions and Identities|
|Content Mode:||Text, Videos and PDF|
|Academic Session:||CBSE 2023-24|
|Medium:||English and Hindi Medium|
Class 8 Maths Chapter 8 Exercise 8.4 Solution
Class VIII Maths NCERT textbook chapter 8 Ex. 8.4 solutions Algebraic Expressions and Identities updated for CBSE academic session 2023-24. Videos related to each question are given with PDF solutions free to use without any login. Exercise 8.4 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 NCERT exercise 8.4 are given here with solution with simple method.
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
If x is a variable and m, n are positive integers such that m > n then
Xᵐ/xⁿ = xᵐ⁻ⁿ
Division of a Monomial by a Monomial
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
(i) (8x² y³)/-2xy = (8/-2) (x²⁻¹ y³⁻¹
(ii) (-15x³ yz³)/-5xyz² = (-15/-5) (x³⁻¹ y1-1 z³⁻²)
= 3x² z
Division of a Polynomial by a Monomial
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
What is the main concept of class 8 Maths exercise 8.4?
The main concept of 8th Maths exercise 8.4 is the division of polynomial. The concepts given in ex. 8.4 are as follows:
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 different ways given in 8th Maths exercise 8.4 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.
What is the significance of exercise 8.4 of 8th mathematics in daily 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.