Class 8 RD Sharma Solutions Chapter 8 Division Of Algebraic Expressions  Exercise 8.2 (original) (raw)

Last Updated : 20 Sep, 2024

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.