Exercise 3.3 - Chapter 3 Algebra Term 2 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $3.3$
Question $1 .$
Fill in the blanks.
(i) The degree of the term $a^{3} b^{2} c^{4} d^{2}$ is
(ii) Degree of the constant term is
(iii) The coefficient of leading term of the expression $3 z^{2} y+2 x-3$ is
Answers:
(i) 11
(ii) 0
(iii) 3

Question 2 .
Say True or False.
(i) The degree of $m^{2} n$ and $m n^{2}$ are equal.
(ii) $7 \mathrm{a}^{2} \mathrm{~b}$ and $-7 \mathrm{ab}^{2}$ are like terms.
(iii) The degree of the expression $-4 x^{2} y z$ is $-4$
(iv) Any integer can be the degree of the expression.
Answers:
(i) True
(ii) False
(iii) False
(iv) True

Question $3 .$
Find the degree of the following terms.

(i) $5 x^{2}$
(ii) $-7 \mathrm{ab}$
(iii) $12 \mathrm{pq}^{2} \mathrm{r}^{2}$
(iv) $-125$
(v) $3 \mathrm{z}$
Solution:
(i) $5 x^{2}$
In $5 x^{2}$, the exponent is 2 . Thus the degree of the expression is 2 .
(ii) $-7 \mathrm{ab}$
In $-7 \mathrm{ab}$, the sum of powers of $\mathrm{a}$ and $\mathrm{b}$ is 2 . (That is $1+1=2$ ).
Thus the degree of the expression is 2 .
(iii) $12 \mathrm{pq}^{2} \mathrm{r}^{2}$
In $12 \mathrm{pq}^{2} \mathrm{r}^{2}$, the sum of powers of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ is 5 . (That is $1+2+2=5$ ).
Thus the degree of the expression is 5 .
(iv) $-125$
Here $-125$ is the constant term. Degree of constant term is 0 .
$\therefore$ Degree of $-125$ is 0 .
(v) $3 z$
The exponent is $3 z$ is 1 .
Thus the degree of the expression is 1 .
 

Question $4 .$
Find the degree of the following expressions.
(i) $x^{3}-1$
(ii) $3 x^{2}+2 x+1$
(iii) $3 \mathrm{t}^{4}-5 \mathrm{st}^{2}+7 \mathrm{~s}^{2} \mathrm{t}^{2}$
(iv) $5-9 y+15 y 2-6 y 3$
(v) $u^{5}+u^{4} v+u^{3} v^{2}+u_{2} v^{3}+u v^{4}$

Solution:
(i) $x^{3}-1$
The terms of the given expression are $x^{3},-1$
Degree of each of the terms: 3,0
Terms with highest degree: $x^{3}$.
Therefore, degree of the expression is $3 .$
(ii) $3 x^{2}+2 x+1$
The terms of the given expression are $3 x^{2}, 2 x, 1$
Degree of each of the terms: $2,1,0$
Terms with highest degree: $3 \mathrm{x}^{2}$
Therefore, degree of the expression is 2 .
(iii) $3 \mathrm{t}^{4}-5 \mathrm{st}^{2}+7 \mathrm{~s}^{2} \mathrm{t}^{2}$
The terms of the given expression are $3 t^{4},-5 s t^{2}, 7 s^{3} t^{2}$
Degree of each of the terms: $4,3,5$
Terms with highest degree: $7 \mathrm{~s}^{2} \mathrm{t}^{2}$
Therefore, degree of the expression is $5 .$
(iv) $5-9 y+15 y^{2}-6 y^{3}$
The terms of the given expression are $5,-9 \mathrm{y}, 15 \mathrm{y}^{2},-6 \mathrm{y}^{3}$
Degree of each of the terms: $0,1,2,3$
Terms with highest degree: $-6 y^{3}$
Therefore, degree of the expression is 3 .

(v) $u^{5}+u^{4} v+u^{3} v^{2}+u_{2} v^{3}+u v^{4}$
The terms of the given expression are $u^{5}, u^{4} v, u^{3} v^{2}, u^{2} v^{3}, u v^{4}$
Degree of each of the terms: $5,5,5,5,5$
Terms with highest degree: $u^{5}, u^{4} v, u^{3} v^{2}, u^{2} v^{3}, u v^{4}$
Therefore, degree of the expression is $5 .$
 

Question 5 .
Identify the like terms : $12 x^{3} y^{2} z,-y^{3} x^{2} z, 4 z^{3} y^{2} x, 6 x^{3} z^{2} y,-5 y^{3} x^{2} z$
Solution:
$-y^{3} x^{2} z$ and $-5 y^{3} x^{2} z$ are like terms.

Question $6 .$
Add and find the degree of the following expressions.
(i) $(9 x+3 y)$ and $(10 x-9 y)$
(ii) $\left(\mathrm{k}^{2}-25 \mathrm{k}+46\right)$ and $\left(23-2 \mathrm{k}^{2}+21 \mathrm{k}\right)$
(iii) $\left(3 m^{2} n+4 p q^{2}\right)$ and $\left(5 n m^{2}-2 q^{2} p\right)$
Solution:
(i) $(9 x+3 y)$ and $(10 x-9 y)$
This can be written as $(9 x+3 y)+(10 x-9 y)$
Grouping the like terms, we get
$(9 x+10 x)+(3 y-9 y)=x(9+10)+y(3-0)=19 x+y(-6)=19 x-6 y$
Thus degree of the expression is $1 .$

(ii) $\left(\mathrm{k}^{2}-25 \mathrm{k}+46\right)$ and $\left(23-2 \mathrm{k}^{2}+21 \mathrm{k}\right)$
This can be written as $\left(\mathrm{k}^{2}-25 \mathrm{k}+46\right)+\left(23-2 \mathrm{k}^{2}+21 \mathrm{k}\right)$
Grouping the like terms, we get
$\begin{aligned}
&\left(k^{2}-2 k^{2}\right)+(-25 k+21 k)+(46+23) \\
&=k^{2}(1-2)+k(-25+21)+69=-1 k^{2}-4 k+69
\end{aligned}$
Thus degree of the expression is 2 .
(iii) $\left(3 m^{2} n+4 p q^{2}\right)$ and $\left(5 n m^{2}-2 q^{2} p\right)$
This can be written as $\left(3 \mathrm{~m}^{2} \mathrm{n}+4 \mathrm{pq}^{2}\right)+\left(5 \mathrm{~nm}^{2}-2 \mathrm{q}^{2} \mathrm{p}\right)$
Grouping the like terms, we get
$\left(3 m^{2} n+5 m^{2} n\right)+\left(4 p q^{2}-2 p q^{2}\right)$
$=\mathrm{m}^{2} \mathrm{n}(3+5)+\mathrm{pq}^{2}(4-2)=8 \mathrm{~m}^{2} \mathrm{n}+2 \mathrm{pq}^{2}$
Thus degree of the expression is $3 .$

Question $7 .$
Simplify and find the degree of the following expressions.
(i) $10 x^{2}-3 x y+9 y^{2}-\left(3 x^{2}-6 x y-3 y^{2}\right)$
(ii) $9 a^{4}-6 a^{3}-6 a^{4}-3 a^{2}+7 a^{3}+5 a^{2}$
(iii) $4 x^{2}-3 x-\left[8 x-\left(5 x^{2}-8\right)\right]$
Solution:
(i) $10 x^{2}-3 x y+9 y^{2}-\left(3 x^{2}-6 x y-3 y^{2}\right)$
$=10 x^{2}-3 x y+9 y^{2}+\left(-3 x^{2}+6 x y+3 y^{2}\right)$
$=10 x^{2}-3 x y+9 y^{2}-3 x^{2}+6 x y+3 y^{2}$
$=\left(10 x^{2}-3 x^{2}\right)+(-3 x y+6 x y)+\left(9 y^{2}+3 y^{2}\right)$
$=x^{2}(10-3)+x y(-3+6)+y^{2}(9+3)$
$=x^{2}(7)+x y(3)+y^{2}(12)$
Hence, the degree of the expression is 2 .

(ii) $9 a^{4}-6 a^{3}-6 a^{4}-3 a^{2}+7 a^{3}+5 a^{2}$
$\begin{aligned}
&=\left(9 a^{4}-6 a^{4}\right)+\left(-6 a^{3}+7 a^{3}\right)+\left(-3 a^{2}+5 a^{2}\right) \\
&=a^{4}(9-6)+a^{3}(-6+7)+a^{2}(-3+5) \\
&=3 a^{4}+a^{3}+2 a^{2}
\end{aligned}$
(iii) $4 x^{2}-3 x-\left[8 x-\left(5 x^{2}-8\right)\right]$
$\begin{aligned}
&\left.=4 x^{2}-3 x-\left[8 x+-5 x^{2}+8\right)\right] \\
&=4 x^{2}-3 x-\left[8 x-5 x^{2}-8\right] \\
&=4 x^{2}-3 x-8 x+5 x^{2}-8 \\
&\left(4 x^{2}+5 x^{2}\right)+(-3 x-8 x)-8 \\
&=x^{2}(4+5)+x(-3-8)-8 \\
&=x^{2}(9)+x(-11)-8 \\
&=9 x^{2}-11 x-8
\end{aligned}$
Hence, the degree of the expression is $2 .$
 

Objective Type Question
Question $8 .$
$3 p^{2}-5 p q+2 q^{2}+6 p q-q^{2}+p q$ is a
(i) Monomial
(ii) Binomial
(iii) Trinomial
(iv) Quadrinomial

Answer:

(iii) Trinomial

Question 9 .
The degree of $6 x^{7}-7 x^{3}+4$ is
(i) 7
(ii) 3
(iii) 6
(iv) 4
Answer:
(i) 7

Question 10 .
If $p(x)$ and $q(x)$ are two expressions of degree 3 , then the degree of $p(x)+q(x)$ is
(i) 6
(ii) 0
(iii) 3
(iv) Undefined
Answer:
(iii) 3