NCERT Solutions for Class 8 Maths Chapter 8 - Algebraic Expressions and Identities Exercise 8.1

Exercise 8.1

1. Add the following expressions.

i. Add $ab - bc$, $bc - ca$, and $ca - ab$.

Ans: Write the like terms below each other in separate row and columns and add them.

$\begin{array}{*{20}{c}} {}&{ab}& - &{bc}&{}&{} \\ + &{}&{}&{bc}& - &{ca} \\  + &{ - ab}&{}&{}& + &{ca} \\ \hline {}&{}&{}&0&{}&{} \end{array}$

ii. Add $a - b + ab$,$b - c + bc$, $c - a - ac$.

Ans: Write the like terms below each other in separate row and columns and add them.

$\begin{array}{*{20}{c}} {}&a& - &b& + &{ab}&{}&{}&{}&{}&{}&{} \\ + &{}&{}&b&{}&{}& - &c& + &{bc}&{}&{} \\ + &{ - a}&{}&{}&{}&{}&{}&c&{}&{}& + &{ac} \\ \hline {}&{}&{}&{}&{}&{ab}&{}&{}& + &{bc}& + &{ac} \end{array}$

The addition of the terms is $ab + bc + ac$.

(iii) ${\text{2}}{{\text{p}}^{\text{2}}}{{\text{q}}^{\text{2}}}{\text{ - 3pq + 4,5 + 7pq - 3}}{{\text{p}}^{\text{2}}}{{\text{q}}^{\text{2}}}$

Ans: 

$ {\text{     2}}{{\text{p}}^{\text{2}}}{{\text{q}}^{\text{2}}}{\text{  - 3pq  + 4}} $

$  {\text{ +    - 3}}{{\text{p}}^{\text{2}}}{{\text{q}}^{\text{2}}}{\text{ + 7pq + 5}}$

$  \overline {{\text{     - }}{{\text{p}}^{\text{2}}}{{\text{q}}^{\text{2}}}{\text{   + 4pq    + 9}}}$

Therefore, the sum of given expressions is ${\text{ - }}{{\text{p}}^{\text{2}}}{{\text{q}}^{\text{2}}}{\text{ + 4pq  + 9}}$

(iv) ${{\text{l}}^{\text{2}}}{\text{ + }}{{\text{m}}^{\text{2}}}{\text{,}}{{\text{m}}^{\text{2}}}{\text{ + }}{{\text{n}}^{\text{2}}}{\text{,}}{{\text{n}}^{\text{2}}}{\text{ + }}{{\text{l}}^{\text{2}}}{\text{,2lm + 2mn + 2nl}}$

Ans:  

$  {\text{      }}{{\text{l}}^{\text{2}}}{\text{ + }}{{\text{m}}^{\text{2}}} $

$  {\text{  +           }}{{\text{m}}^{\text{2}}}{\text{ +  }}{{\text{n}}^{\text{2}}} $

$  {\text{ +    }}{{\text{l}}^{\text{2}}}{\text{           +  }}{{\text{n}}^{\text{2}}} $

$  {\text{ +                             2lm + 2mn + 2nl}} $

$  \overline {{\text{    2}}{{\text{l}}^{^{\text{2}}}}{\text{ + 2}}{{\text{m}}^{\text{2}}}{\text{ + 2}}{{\text{n}}^{\text{2}}}{\text{ + 2lm + 2mn + 2nl}}}  $

Therefore, the sum of the given expressions is ${\text{2}}{{\text{l}}^{^{\text{2}}}}{\text{ + 2}}{{\text{m}}^{\text{2}}}{\text{ + 2}}{{\text{n}}^{\text{2}}}{\text{ + 2lm + 2mn + 2nl}}$

2. Subtract the following expressions.

a. Subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$.

Ans:Write the like terms below each other and find the difference.

$\begin{array}{*{20}{c}} {}&{12a}& - &{9ab}& + &{5b}& - &3 \\ {}&{4a}& - &{7ab}& + &{3b}& + &{12} \\ {\left(  -  \right)}&{}&{\left(  +  \right)}&{}&{\left(  -  \right)}&{}&{\left(  -  \right)}&{} \\ \hline {}&{8a}& - &{2ab}& + &{2b}& - &{15} \end{array}$

The difference is $8a - 2ab + 2b - 15$.

b. Subtract $3xy + 5yz - 7zx$ from $5xy - 2yz - 2zx + 10xyz$.

Ans:Write the like terms below each other and find the difference.

$\begin{array}{*{20}{c}}{}&{5xy}& - &{2yz}& - &{2zx}& + &{10xyz} \\ {}&{3xy}& + &{5yz}& - &{7zx}&{}&{} \\ {\left(  -  \right)}&{}&{\left(  -  \right)}&{}&{\left(  +  \right)}&{}&{}&{} \\ \hline {}&{2xy}& - &{7yz}& + &{5zx}& + &{10xyz} \end{array}$

The difference is $2xy - 7yz + 5zx + 10xyz$.

c. Subtract \[4{p^2}q - 3pq + {\text{ }}5p{q^2} - 8p + 7q - 10\] from \[18 - 3p - 11q + 5pq - 2p{q^2} + 5{p^2}q\].

Ans:Write the like terms below each other and find the difference.

$\begin{array}{*{20}{c}} {}&{18}& - &{3p}& - &{11q}& + &{5pq}& - &{2p{q^2}}& + &{5{p^2}q} \\ {}&{ - 10}& - &{8p}& + &{7q}& - &{3pq}& + &{5p{q^2}}& + &{4{p^2}q} \\ {\left(  +  \right)}&{}&{\left(  +  \right)}&{}&{\left(  -  \right)}&{}&{\left(  +  \right)}&{}&{\left(  -  \right)}&{}&{\left(  -  \right)}&{} \\ \hline {}&{28}& + &{5p}& - &{18q}& + &{8pq}& - &{7p{q^2}}& + &{{p^2}q} \end{array}$

The difference is $28 + 5p - 18q + 8pq - 7p{q^2} + {p^2}q$.

Conclusion

NCERT Solutions for Class 8 Maths Chapter 8 - Algebraic Expressions and Identities Exercise 8.1, provided by Vedantu, offers clear and detailed explanations of fundamental algebraic concepts. It is important to focus on understanding the definitions and properties of terms, coefficients, and variables. Combining like terms and simplifying expressions are key skills emphasized in class 8 ex 8.1. Vedantu’s expert solutions make these concepts easy to grasp and apply. Regular practice with these solutions will build a strong foundation in algebra, preparing students for more advanced mathematical topics in the future.

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.