class 8 maths exercise 9.2 solutions Answer worksheet pdf notes 2023

Class 8 Maths Exercise 9.2 Solutions │ exercise 9.2 class 8 Question 1 2 3 4 5  Solution worksheet pdf notes mcq 2023

Exercise 9.2 Solutions (toc)

exercise 9.1 class 8 question 1

1. Find the product of the following pairs of monomials.

(i) 4, 7p

(ii) – 4p, 7p

(iii) – 4p, 7pq

(iv) 4p3, – 3p

(v) 4p, 0

class 8 maths exercise 9.1 solutions Answer

(i) $4\times 7�=28�$

This means you multiply the number 4 by the number 7, and since there's a variable $�$, you just write it down as $28�$.

(ii) $(-4�)\times (7�)=-28{�}^2$

Here, you're multiplying $-4�$ by $7�$. First, you multiply the numbers (-4 and 7) to get -28. Then, because there are two $�$ variables, you add the exponents, which gives you ${�}^2$, so the answer is $-28{�}^2$.

(iii) $(-4�)\times (7��)=-28{�}^2�$

Similar to the last one, you multiply the numbers (-4 and 7) to get -28. Then, you have one $�$ and one $�$, so you write ${�}^2�$.

(iv) $4{�}^3\times (-3�)=-12{�}^4$

In this case, you multiply 4 by -3 to get -12. Then, you have ${�}^3$ and $�$, so you add the exponents to get ${�}^4$, giving you $-12{�}^4$.

(v) $4�\times 0=0$

Whenever you multiply anything by 0, the answer is always 0. So, in this case, $4�$ multiplied by 0 is 0.

exercise 9.1 class 8 question 2

2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths, respectively.

(p, q) ; (10m, 5n) ; (20x² , 5y²) ; (4x, 3x²) ; (3mn, 4np)

exercise 9.1 class 8 question 2 solution

To find the area of a rectangle, you multiply the length by the breadth. The formulas for the areas of rectangles with the given pairs of monomials as lengths and breadths are as follows:

(i) $\text{Area}=�\times �$

(ii) $\text{Area}=10�\times 5�$

(iii) $\text{Area}=20{�}^2\times 5{�}^2$

(iv) $\text{Area}=4�\times 3{�}^2$

(v) $\text{Area}=3��\times 4��$

Now, let's calculate each of these:

(i) $\text{Area}=�\times �$

(ii) $\text{Area}=10�\times 5�=50��$

(iii) $\text{Area}=20{�}^2\times 5{�}^2=100{�}^2{�}^2$

(iv) $\text{Area}=4�\times 3{�}^2=12{�}^3$

(v) $\text{Area}=3��\times 4��=12{�}^2{�}^2$

So, the areas of the rectangles with the given pairs of monomials as their lengths and breadths are:

(i) $��$

(ii) $50��$

(iii) $100{�}^2{�}^2$

(iv) $12{�}^3$

(v) $12{�}^2{�}^2$

exercise 9.1 class 8 question 3

3. Complete the following table of products:

exercise 9.1 class 8 question 3 solution

exercise 9.1 class 8 question 4

4. Obtain the volume of rectangular boxes with the following length, breadth and height, respectively .

(i) 5a, 3a², 7a⁴

(ii) 2p, 4q, 8r

(iii) xy, 2x²y, 2xy²

(iv) a, 2b, 3c

exercise 9.1 class 8 question 4 solution

(i) $\text{Volume}=5�\times 3{�}^2\times 7{�}^4$

(ii) $\text{Volume}=2�\times 4�\times 8�$

(iii) $\text{Volume}=��\times 2{�}^2�\times 2�{�}^2$

(iv) $\text{Volume}=�\times 2�\times 3�$

Now, let's calculate each of these:

(i) $\text{Volume}=5�\times 3{�}^2\times 7{�}^4=105{�}^7$

(ii) $\text{Volume}=2�\times 4�\times 8�=64���$

(iii) $\text{Volume}=��\times 2{�}^2�\times 2�{�}^2=4{�}^4{�}^4$

(iv) $\text{Volume}=�\times 2�\times 3�=6���$

So, the volumes of the rectangular boxes with the given sets of monomials as their lengths, breadths, and heights are:

(i) $105{�}^7$

(ii) $64���$

(iii) $4{�}^4{�}^4$

(iv) $6���$

exercise 9.1 class 8 question 5

5. Obtain the product of

(i) $��,��,��$

(ii) $�,-{�}^2,{�}^3$

(iii) $2,4�,8{�}^2,16{�}^3$

(iv) $�,2�,3�,6���$

(v) $�,-��,���$

exercise 9.1 class 8 question 5 solution

(i) For $��\times ��\times ��$, you can multiply the coefficients (numbers) together and then multiply the variables together. So, $��\times ��\times ��=�\times �\times �\times �\times �\times �={�}^2{�}^2{�}^2$.

(ii) For $�\times -{�}^2\times {�}^3$, again, multiply the coefficients and the variables separately. So, $�\times -{�}^2\times {�}^3=-{�}^{1+2+3}=-{�}^6$.

(iii) For $2\times 4�\times 8{�}^2\times 16{�}^3$, multiply the coefficients and the variables. $2\times 4\times 8\times 16=1024$, and $�\times {�}^2\times {�}^3={�}^{1+2+3}={�}^6$. So, the result is $1024{�}^6$.

(iv) For $�\times 2�\times 3�\times 6���$, multiply the coefficients and variables separately. $�\times 2\times 3\times 6=36$, and $�\times �\times ���={�}^2�{�}^2$. So, the result is $36{�}^2�{�}^2$.

(v) For $�\times -��\times ���$, multiply the coefficients and the variables. $�\times -�\times �\times �\times �=-{�}^2��$.

Class 8 Maths Exercise 9.1 Solutions