Ncert Math Solution Class 8 Chapter 9.4
CBSE NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.4 (Ex. 9.4) Algebraic Expressions and Identities updated for CBSE academic session 2021-2022. 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 |
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CBSE NCERT Class 8 Maths Chapter 9 Exercise 9.4 Solution in Hindi and English Medium
- Class 8 Maths Chapter 9 Exercise 9.4 Solution in English Medium
- Class 8 Maths Chapter 9 Exercise 9.4 Solution in Hindi Medium
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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.
Ncert Math Solution Class 8 Chapter 9.4
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