# CBSE NCERT Solutions for Class 8 Chapter 9

NCERT Solutions are the most important and foremost tool to look up to especially when students are preparing for school and competitive examinations. Students are advised to practice the NCERT questions and solutions for class 8 on a regular basis to score well in their class 8 exam.

CBSE NCERT Solutions for Class 8 Maths Chapter 9:

Question-1:

(i) ab – bc, bc – ca, ca – ab
(ii) a – b + ab, b – c + bc, c – a + ac
(iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl

Solution:

i) (ab - bc) + (bc - ca) + (ca-ab)
= ab - bc + bc - ca + ca-ab
= ab-ab –bc +bc –ca+ca
= 0
ii) (a - b + ab) + (b - c + bc) + (c - a + ac)
= a - b + ab + b - c + bc + c - a + ac
= a- a +b – b +c – c + ab + bc + ca
=0+0 +0+ ab + bc + ca
= ab + bc + ca
iii) 2p2q2 – 3pq + 4, 5 + 7pq – 3p2q2
= (2p2q2 - 3pq + 4) + (5 + 7pq - 3p2q2)
= 2p2q2 - 3p2q2 - 3pq + 7pq + 4 + 5
= - p2q2 + 4pq + 9
iv) (l2 + m2) + (m2 + n2) + (n2 + l2) + (2lm + 2mn + 2nl)
= l2 + l2 + m2 + m2 + n2 + n2 + 2lm + 2mn + 2nl
= 2l2 + 2m2 + 2n2 + 2lm + 2mn + 2nl

Question-2:

(a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
(c) Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q

Solution:

a) (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)
= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12
=12a – 4a -9ab + 7ab +5b – 3b -3 -12
= 8a - 2ab + 2b - 15
b) (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)
= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx
=5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz
= 2xy - 7yz + 5zx + 10xyz
c) (18 - 3p - 11q + 5pq - 2pq2 + 5p2q) - (4p2q - 3pq + 5pq2 - 8p + 7q - 10)
= 18 - 3p - 11q + 5pq - 2pq2 + 5p2q - 4p2q + 3pq - 5pq2 + 8p - 7q + 10
=18+10 -3p+8p -11q – 7q + 5 pq+ 3pq- 2pq^2 – 5pq^2 + 5 p^2 q – 4p^2 q
= 28 + 5p - 18q + 8pq - 7pq2 - p2q

Question-3:

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i) 5a, 3a2, 7a8
(ii) (2p, 4q, 8r)
(iii) xy, 2x2y, 2xy2
(iv) a, 2b, 3c

Solution:

volume of rectangular box is given by Volume = length x breadth x height
(i) 5a x 3a2 x 7a8 = (5 37) (a * a^2 * a^8 ) =105a11 cubic units
(ii) 2p x 4q x 8r = (2 4 8 ) (p qr ) = 64pqr cubic units
(iii) y * 2x2y * 2xy2 =(1
2
2 )( x* x^2 x yyy^2 ) = 4x4y4 cubic units
(iv) a x 2b x 3c = (123 ) (abc) = 6abc cubic units