Exercise 8.2 (Revised) - Chapter 9 - Algebraic Expressions & Identities - Ncert Solutions class 8 - Maths

You can Download the Exercise 8.2 (Revised) - Chapter 9 - Algebraic Expressions & Identities - Ncert Solutions class 8 - Maths with expert answers for all chapters. Perfect for Tamil & English Medium students to revise the syllabus and score more marks in board exams. Download and share it with your friends

Share this to Friend on WhatsApp

Chapter 8 - Algebraic Expressions & Identities - NCERT Solutions for Class 8 Maths

Ex 8.2 Question 1.

Find the product of the following pairs of monomials:
(i) $4,7 p$
(ii) $-4 p, 7 p$
(iii) $-4 p, 7 p q$
(iv) $4 p^3=-3 p$
(iv) $4 p, 0$

Answer.
(i) $4 \times 7 p=4 \times 7 \times p=28 p$
(ii) $-4 p \times 7 p=(-4 \times 7) \times(p \times p)$
$
=-28 p^2
$
(iii) $-4 p \times 7 p q=(-4 \times 7)(p \times p q)$
$
=-28 p^2 q
$
(iv) $4 p^3 \times-3 p=(4 \times-3)\left(p^3 \times p\right)$
$
=-12 p^4
$

(v) $4 p \times 0=(4 \times 0)(p)=0$
Ex 8.2 Question 2.

Find the areas of rectangles with the following pairs of monomials as their lengths

and breadths respectively:
$
(p, q) ;(10 m, 5 n) ;\left(20 x^2, 5 y^2\right) ;\left(4 x, 3 x^2\right) ;(3 m n, 4 n p)
$

Answer.
(i) Area of rectangle
$
\begin{aligned}
& =\text { length } \times b \text { readth } \\
& =p \times q=p q \text { sq. units }
\end{aligned}
$
(ii) Area of rectangle
$
\begin{aligned}
& =\text { length } \times \text { readth } \\
& =10 \mathrm{~m} \times 5 \mathrm{n}=(10 \times 5)(\mathrm{m} \times \mathrm{n}) \\
& =50 \mathrm{mn} \text { sq. units }
\end{aligned}
$
(iii) Area of rectangle $=$ length $\times$ breadth
$
\begin{aligned}
& =20 x^2 \times 5 y^2=(20 \times 5)\left(x^2 \times y^2\right) \\
& =100 x^2 y^2 \text { sq. units }
\end{aligned}
$
(iv) Area of rectangle $=$ length $\times$ breadth

$\begin{aligned}
&\begin{aligned}
& =4 x \times 3 x^2=(4 \times 3)\left(x \times x^2\right) \\
& =12 x^3 \text { sq. units }
\end{aligned}\\
&\begin{aligned}
& \text { (v) Area of rectangle = length } \times \text { reaadth } \\
& =3 m n \times 4 n p=(3 \times 4)(m n \times n p) \\
& =12 m n^2 p \text { sq. units }
\end{aligned}
\end{aligned}$

Ex 8.2 Question 3.

Complete the table of products:
(i)

Answer.
(i)

Ex 8.2 Question 4.

Obtain the volume of rectangular boxes with the following length, breadth and height respectively:
(i) $5 a, 3 a^2 7 a^4$
(ii) $2 p, 4 q, 8 r$

(iii) $x y, 2 x^2 y, 2 x y^2$
(iv) $a, 2 b, 3 c$

Answer.

(i) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { breadth } \times \text { height } \\
& =5 a \times 3 a^2 \times 7 a^4=(5 \times 3 \times 7)\left(a \times a^2 \times a^4\right) \\
& =105 a^7 \text { cubic units }
\end{aligned}
$
(ii) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { breadth } \times \text { height } \\
& =2 p \times 4 q \times 8 r=(2 \times 4 \times 8)(p \times q \times r) \\
& =64 p q r \text { cubic units }
\end{aligned}
$
(iii) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { breadth } \times \text { height } \\
& =x y \times 2 x^2 y \times 2 x y^2 \\
& =(1 \times 2 \times 2)\left(x \times x^2 \times x \times y \times y \times y^2\right)
\end{aligned}
$

(iii) $x y, 2 x^2 y, 2 x y^2$
(iv) $a, 2 b, 3 c$

Answer.

(i) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { breadth } \times \text { height } \\
& =5 a \times 3 a^2 \times 7 a^4=(5 \times 3 \times 7)\left(a \times a^2 \times a^4\right) \\
& =105 a^7 \text { cubic units }
\end{aligned}
$
(ii) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { breadth } \times \text { height } \\
& =2 p \times 4 q \times 8 r=(2 \times 4 \times 8)(p \times q \times r) \\
& =64 p q r \text { cubic units }
\end{aligned}
$
(iii) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { breadth } \times \text { height } \\
& =x y \times 2 x^2 y \times 2 x y^2 \\
& =(1 \times 2 \times 2)\left(x \times x^2 \times x \times y \times y \times y^2\right)
\end{aligned}
$

$
=4 x^4 y^4 \text { cubic units }
$
(iv) Volume of rectangular box
$
\begin{aligned}
& =\text { length } \times \text { readth } \times \text { height } \\
& =a \times 2 b \times 3 c=(1 \times 2 \times 3)(a \times b \times c) \\
& =6 a b c \text { cubic units }
\end{aligned}
$
Ex 8.2 Question 5.

Obtain the product of:

(i) $x y, y z, z x$
(ii) $a=-a^2, a^3$
(iii) $2,4 y, 8 y^2, 16 y^3$
(iv) $a, 2 b, 3 c, 6 a b c$
(v) $m_2-m n_2 m n p$

Answer.
$
\begin{aligned}
& \text { (i) } x y \times y z \times z x=x \times x \times y \times y \times z \times z \\
& =x^2 y^2 z^2
\end{aligned}
$
(ii) $a \times\left(-a^2\right) \times a^3=(-1)\left(a \times a^2 \times a^3\right)$
$
=-a^6
$
$
\begin{aligned}
& \text { (iii) } 2 \times 4 y \times 8 y^2 \times 16 y^3 \\
& =(2 \times 4 \times 8 \times 16)\left(y \times y^2 \times y^3\right) \\
& =1024 y^6
\end{aligned}
$
(iv) $a \times 2 b \times 3 c \times 6 a b c$
$
=(1 \times 2 \times 3 \times 6)(a \times b \times c \times a b c)
$

$
=36 a^2 b^2 c^2
$
(v) $m \times-m n \times m \eta p=(-1)(m \times m \times m \times n \times n \times p)$
$
=-m^3 n^2 p
$