Class 8 RD Sharma Solutions - Chapter 8 Division Of Algebraic Expressions - Exercise 8.2

Chapter 8 of RD Sharma's Class 8 mathematics textbook covers Division of Algebraic Expressions. Exercise 8.2 typically focuses on the division of polynomials by monomials. This exercise helps students understand how to divide a polynomial by a single term, reinforcing their understanding of exponent rules and algebraic manipulation.

Question 1. Divide 6x³y²z² by 3x²yz

Solution:

We can write 6x³y²z² as 2 * 3 * x * x * x * y * y * z * z

We can write 3x²yz as 3 * x * x * y * z

Now ans = (6x³y²z²)/(3x²yz)

              = (2 * 3 * x * x * x * y * y * z * z)/(3 * x * x * y * z)

              = 2 * x * y * z

So the answer is 2xyz

Question 2. Divide 15m²n³ by 5m²n²

Solution:

We can write 15m²n³ as 5 * 3 * m * m * n * n * n

We can write 5m²n² as 5 * m * m * n * n

Now ans = (15m²n³)/(5m²n²)

              = (3 * 5 * m * m * n * n * n)/(5 * m * m * n * n)

             = 3 * n

So the answer is 3n

Question 3. Divide 24a³b³ by -8ab

Solution:

We can write 24a³b³ as 3 * 8 * a * a * a * b * b * b

Now ans = (24a³b³)/(-8ab)

              = -(3 * 8 * a * a * a * b * b * b)/(8 * a * b)

              = -(3 * a * a * b * b)

              = -3 * a * a * b * b

We can write -3 * a * a * b * b as -3 * a² * b²

So  the answer is -3a²b²

Question 4. Divide -21abc² by 7abc

Solution:

We can write -21abc² as -3 * 7 * a * b * c * c

We can write 7abc as 7 * a * b * c

Now ans = (-21abc²)/(7abc)

             = -(7 * 3 * a * b * c * c)/(7 * a * b * c)

             = -(3 * c)

             = -3c

So the answer is -3c

Question 5. Divide 72xyz² by -9xz

Solution:

We can write 72xyz² as 8 * 9 * x * y * z * z

Now ans = (72xyz²)/(-9xz)

              = -(8 * 9 * x * y * z * z)/(9 * x * z)

              = -(8 * y * z)

              = -8yz

So the answer is -8yz

Question 6. Divide -72a⁴b⁵c⁸ by -9a²b²c³

Solution:

We can write -72a⁴b⁵c⁸ as -8*9*a*a*a*a*b*b*b*b*b*c*c*c*c*c*c*c*c

We can write -9a²b²c³ as -9*a*a*b*b*c*c*c

Now ans = (-72a⁴b⁵c⁸) /(-9a²b²c³)

              = (8*9*a*a*a*a*b*b*b*b*b*c*c*c*c*c*c*c*c) / (9*a*a*b*b*c*c*c)

              = (8*a*a*b*b*b*c*c*c*c*c)

              = 8*a*a*b*b*b*c*c*c*c*c

We can write 8*a*a*b*b*b*c*c*c*c*c as 8 * a² * b³ * c⁵

So the answer is 8a²b³c⁵

Question 7. Divide 16 * m³ * y² by 4 * m² * y

Solution:

We can write 16m³y² as 4 * 4 * m * m * m * y * y

We can write 4m²y as 4 * m * m * y

Now ans = (16m³y²)/(4m²y)

              = (4 * 4 * m * m * m * y * y)/(4 * m * m * y)

              = (4 * m * y)

              = 4my

So the answer is 4my

Question 8. Divide 32 * m² * n³ * p² by 4 * m * n * p

Solution:

We can write 32m²n³p² as 4 * 8 * m * m * n * n * n * p * p

Now ans = (32m²n³p²) / (4mnp)

              = (4 * 8 * m * m * n * n * n * p * p) / (4 * m * n * p))

              = (8 * m * n * n * p)

We can write 8 * m * n * n * p as 8 * m * n² * p

So the answer is 8mn²p.

Summary

Exercise 8.2 in Chapter 8 of RD Sharma's Class 8 mathematics textbook focuses on the division of polynomials by monomials. This exercise builds upon students' previous knowledge of algebraic operations and exponent rules. Through a series of problems, students learn to divide each term of the polynomial by the monomial divisor, applying the rules of exponents and simplifying the resulting expressions. The problems in this set gradually increase in complexity, involving various variables and exponents. By practicing these divisions, students enhance their algebraic manipulation skills, reinforce their understanding of exponent properties, and prepare for more advanced polynomial operations. This exercise is crucial for developing a strong foundation in algebra, as the skills learned here are fundamental to more complex algebraic manipulations, factoring techniques, and solving polynomial equations in higher mathematics.