NCERT Solutions for Class 8 Maths Chapter 8 - Algebraic Expressions and Identities Exercise 8.2

Exercise  8.2

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

i. $4$ and $7p$

Ans: The required product is,

$4 \times 7p = 4 \times 7 \times p$

$4 \times 7p = 28p$

ii. $ - 4p$ and $7p$

Ans: The required product is,

$ - 4p \times 7p = \left( { - 4} \right) \times p \times 7 \times p$

$ - 4p \times 7p = \left( { - 4 \times 7} \right) \times \left( {p \times p} \right)$

$ - 4p \times 7p =  - 28{p^2}$

iii. $ - 4p$ and $7pq$

Ans: The required product is,

$ - 4p \times 7pq = \left( { - 4} \right) \times p \times 7 \times p \times q$

$ - 4p \times 7pq = \left( { - 4 \times 7} \right) \times \left( {p \times p} \right) \times q$

$ - 4p \times 7pq =  - 28{p^2}q$

iv. $4{p^3}$ and $ - 3p$

Ans: The required product is,

\[4{p^3} \times \left( { - 3p} \right) = 4 \times {p^3} \times \left( { - 3} \right) \times p\]

$4{p^3} \times \left( { - 3p} \right) = \left( {4 \times  - 3} \right) \times \left( {{p^3} \times p} \right)$

$4{p^3} \times \left( { - 3p} \right) =  - 12{p^4}$

v. $4p$ and $0$

Ans: The required product is,

$4p \times \left( 0 \right) = 4 \times p \times 0$

$4p \times \left( 0 \right) = 0$

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

$\left( {p,q} \right)$;$\left( {10m,5n} \right)$;$\left( {20{x^2},5{y^2}} \right)$;$\left( {4x,3{x^2}} \right)$;$\left( {3mn,4np} \right)$.

Ans: The area of a rectangle is the product of length and breadth.

The first rectangle has dimensions, $\left( {p,q} \right)$. Let the area be ${A_1}$. Thus, ${A_1} = pq$.

The second rectangle has dimensions, $\left( {10m,5n} \right)$. Let the area be ${A_2}$. Thus, ${A_2} = 10m \times 5n$

${A_2} = 10 \times 5 \times m \times n$

${A_2} = 50mn$

The third rectangle has dimensions, $\left( {20{x^2},5{y^2}} \right)$. Let the area be ${A_3}$. Thus, ${A_3} = 20{x^2} \times 5{y^2}$

${A_3} = \left( {20 \times 5} \right) \times \left( {{x^2} \times {y^2}} \right)$

${A_3} = 100{x^2}{y^2}$

The third rectangle has dimensions, $\left( {4x,3{x^2}} \right)$. Let the area be ${A_4}$. Thus, ${A_4} = 4x \times 3{x^2}$

${A_4} = \left( {4 \times 3} \right) \times \left( {x \times {x^2}} \right)$

${A_4} = 12{x^3}$

The third rectangle has dimensions, $\left( {3mn,4np} \right)$. Let the area be ${A_5}$. Thus, ${A_5} = 3mn \times 4np$

${A_5} = \left( {3 \times 4} \right) \times \left( {m \times n \times n \times p} \right)$

${A_5} = 12m{n^2}p$

3. Complete the table of products.

Ans:  Multiply the term in particular row with respective column to complete the table.

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

i. $5a,3{a^2},7{a^4}$

Ans: The volume of a rectangle is the product of length, breadth and height.

The rectangular box has dimensions, $5a$, $7{a^4}$, and $3{a^2}$. Let the volume be ${V_1}$. Thus,${V_1} = 5a \times 3{a^2} \times 7{a^4}$

${V_1} = 5 \times 3 \times 7 \times a \times {a^2} \times {a^4}$

${V_1} = 105{a^7}$

ii. $2p$,$4q$,$8r$

Ans: The rectangular box has dimensions, $2p$,$4q$,$8r$. Let the volume be ${V_2}$. Thus, 

${V_2} = 2p \times 4q \times 8r$

${V_2} = 2 \times 4 \times 8 \times p \times q \times r$

${V_2} = 64pqr$

iii. $xy$,$2{x^2}y$,$2x{y^2}$

Ans: The rectangular box has dimensions, $xy$,$2{x^2}y$,$2x{y^2}$. Let the volume be ${V_3}$. Thus, ${V_3} = xy \times 2{x^2}y \times 2x{y^2}$

${V_3} = 2 \times 2 \times x \times {x^2} \times x \times y \times y \times {y^2}$

${V_3} = 4{x^4}{y^4}$

iv. $a$,$2b$,$3c$

Ans: The rectangular box has dimensions, $a$,$2b$,$3c$. Let the volume be ${V_3}$. Thus, \[{V_4} = a \times 2b \times 3c\]

\[{V_4} = 2 \times 3 \times a \times b \times c\]

\[{V_4} = 6abc\]

5. Obtain the product of the following:

i. $xy$,$yz$,$zx$

Ans: Group the like terms and multiply.

$xy \times yz \times zx = {x^2}{y^2}{z^2}$

ii. $a$,$ - {a^2}$,${a^3}$

Ans: Group the like terms and multiply.

$a \times \left( { - {a^2}} \right) \times {a^3} =  - {a^6}$

iii. $2$,$4y$,$8{y^2}$,$16{y^3}$

Ans: Group the like terms and multiply.

$2 \times 4y \times 8{y^2} \times 16{y^3} = 2 \times 4 \times 8 \times 16 \times y \times {y^2} \times {y^3}$

$2 \times 4y \times 8{y^2} \times 16{y^3} = 1024{y^6}$

iv. $a$,$2b$,$3c$,$6abc$

Ans: Group the like terms and multiply.

$a \times 2b \times 3c \times 6abc = 2 \times 3 \times 6 \times a \times b \times c \times abc$

$a \times 2b \times 3c \times 6abc = 36{a^2}{b^2}{c^2}$

v. $m$,\[ - mn\],$mnp$

Ans: Group the like terms and multiply.

$m \times \left( { - mn} \right) \times mnp = m \times \left( { - m} \right) \times m \times n \times p$

$m \times \left( { - mn} \right) \times mnp =  - {m^3}{n^2}p$

Conclusion

NCERT Class 8 Maths Chapter 8 Exercise 8.2, focuses on understanding the properties and areas of different shapes like parallelograms, rectangles, rhombuses, and squares. It is important to use the correct formulas to find the area of each shape. Pay attention to the sides, angles, and diagonals of these shapes. Practice these concepts regularly to improve your geometry skills and gain confidence. This Class 8 Maths Chapter 8 Exercise 8.2 helps build a strong foundation in understanding the basics of quadrilaterals, which is crucial for further studies in geometry.

Class 8 Maths Chapter 8: Exercises Breakdown

CBSE Class 8 Maths Chapter 8 Other Study Materials

Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.