NCERT Solutions for Class 8 Maths Chapter 9: Algebraic Expressions and Identities - Exercise 9.1

Exercise 9.1

1. Identify the terms, their coefficients for each of the following expressions.

i. $5xy{z^2} - 3zy$

Ans:  The terms are $5xy{z^2}$and $ - 3zy$.The coefficients of $5xy{z^2}$ is $5$, and $ - 3zy$ is $ - 3$.

ii. $1 + x + {x^2}$

Ans:  The terms are $1$, $x$, and ${x^2}$.The coefficient of $1$ is $1$,$x$ is $1$, and ${x^2}$ is $1$.

iii. \[4{x^2}{y^2} - 4{x^2}{y^2} + {z^2}\]

Ans:  The terms are \[4{x^2}{y^2}\], \[ - 4{x^2}{y^2}\], and \[{z^2}\].The coefficient of \[4{x^2}{y^2}\] is $4$,\[ - 4{x^2}{y^2}\] is $ - 4$, and \[{z^2}\] is $1$.

iv. $3 - pq + qr - rp$

Ans:  The terms are $3$, $ - pq$, $qr$ and $ - rp$.The coefficient of$3$ is $1$,$ - pq$ is $1$, $qr$ is $1$, and $ - rp$ is $ - 1$.

v. $\dfrac{x}{2} + \dfrac{y}{2} - xy$

Ans:  The terms are $\dfrac{x}{2}$, $\dfrac{y}{2}$, and $ - xy$.The coefficient of $\dfrac{x}{2}$ is $\dfrac{1}{2}$,$\dfrac{y}{2}$ is $\dfrac{1}{2}$, and $ - xy$ is $ - 1$.

vi. $0.3a - 0.6ab + 0.5b$

Ans:  The terms are $0.3a$, $ - 0.6ab$, and $0.5b$.The coefficients of $0.3a$ is $0.3$,$ - 0.6ab$ is $ - 0.6$, and $0.5b$ is $0.5$.

2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomial do not fit any of these three categories? $x + y$,$1000$,$x + {x^2} + {x^3} + {x^4}$, $7 + y + 5x$, $2y - 3{y^2}$, $2y - 3{y^2} + 4{y^3}$, $5x - 4y + 3xy$, $4z - 15{z^2}$, $ab + bc + cd + da$,$pqr$, ${p^2}q + p{q^2}$,$2p + 3q$.

Ans: The polynomials with only one term are called monomials. The monomials given are $1000$,and$pqr$.

The polynomials with two terms are called binomials. The binomials are, $x + y$,$2y - 3{y^2}$, $4z - 15{z^2}$,${p^2}q + p{q^2}$, and $2p + 3q$.

The polynomials with three terms are called trinomials. The trinomials are, $7 + y + 5x$, $2y - 3{y^2} + 4{y^3}$, $5x - 4y + 3xy$.

The polynomials that do not fit any of the given categories are as follows, 

$x + {x^2} + {x^3} + {x^4}$, $ab + bc + cd + da$.

3. 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 $ab + bc + ac$.

4. 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 $28 + 5p - 18q + 8pq - 7p{q^2} + {p^2}q$.

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities (Ex 9.1) Exercise 9.1

Opting for the NCERT solutions for Ex 9.1 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 9.1 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 8 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 8 Maths Chapter 9 Exercise 9.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

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