physicscatalyst.com logo





Ncert Solutions for Class 8 Mathematics Chapter 14 - Factorization CBSE Exercise 14.1





In this page we have Ncert Solutions for Class 8 Mathematics Chapter 14 - Factorization Chapter 14 for Exercise 14.1 . Hope you like them and do not forget to like , social share and comment at the end of the page.
Question 1
Find the common factors of the given terms.
(i) 12x, 36
(ii) 2y, 22xy
(iii) 14 pq, 28 p2q2
(iv) 2x, 3x², 4
(v) 6 abc, 24ab², 12 a²b
(vi) 16 x³, – 4x², 32x
(vii) 10 pq, 20qr, 30rp
(viii) 3x² y³, 10x³ y²,6 x² y²z
Answer:
1) We need to convert each of these terms in simple factors forms and then choose the common factors
12x =2×2×3×x
36=2×2×3×3
So common Factor are 2,2,3
And  2×2×3=12
2) 2y=2×y
22xy=2×11×y×x
So common factors are 2,y
And 2×y=2y
3) 14 pq= 2×7×p×q
 28 p2q2=2×2×7×p×p×q×q
So common factors are  2,7,p,q
=14pq
4) 2x=2×x
3x2=3×x×x
4=2×2
There is no common factor other than unity, so common factor= 1
5) 6abc=2×3×a×b×c
24ab2=2×2×2×3×a×b×b
12a2b=2×2×3×a×a×b
Common factors are 2, 3, a, b
=6ab
6) 16x3=2×2×2×2×x×x×x
-4x2=-2×2×x×x
32x=-2×2×2×2×2×x
Common factors are 2, 2, x
=4x
7) 10pq=-2×5×p×q
20qr=-2×2×5×q×r
30rp=-2×3×5×p×r
Common factors are 2,5
=10
8) 3x2y3=3×x×x×y×y×y
10x3y3=2×5×x×x×x×y×y×y
6x2y2z=-2×3×x×x×y×y×z
Common factors are x, x, y, y
=x2y2


Question 2
 Factorize the following expressions.
(i) 7x – 42
(ii) 6p – 12q
(iii) 7a² + 14a
(iv) – 16 z + 20 z³
(v) 20 l² m + 30 a l m
(vi) 5 x² y – 15 xy²
(vii) 10 a² – 15 b² + 20 c²
(viii) – 4 a² + 4 ab – 4 ca
(ix) x² y z + x y²z + x y z²
(x) a x² y + b x y² + c x y z²
Answer
In these problem, we need to factorize each term and then find common factors to factorize the expression
1) 7x-42
=  (7×x) – (7×6)
=7(x-6)
2) 6p-12q
=  (6×p) – (6×2q)
=6(p-2q)
3) 7a2+14a
=(7×a×a) +  (2×7×a)
=7a(a+2)
4) -16z+ 20z3
=4z(5z2-4)
5) 20 l² m + 30 a l m
=(2×2×5×l×m×l)  + (2×3×5×a×l×m)
=2lm(10l+15a)
6) 5 x²y -15 xy2
=(5×x×x×y)  + (5×3×x×y×y)
=5x(xy-3y2)
7) 10a² -15 b2+20c2
=(2×5×a×a)  - (5×3×b×b) + (5×2×2×c×c)
=5(2a2-3b2+4c2)
8) -4a² +4a b-4ca
=(-4×a×a)  +(4×b×a) - (4×c×a)
=-4a(a-b+c)
9)  x²yz + xy2z  +xyz2
=(x×x×y×z)  +(x×y×y×z) +(x×y×z×z)
=xyz(x+y+z)
10) ax²yz + bxy2z  +cxyz2
=(x×x×y×z×a)  +(x×y×y×z×b) +(x×y×z×z×c)
=xyz(ax+by+cz)
Question 3
Factorize
(i) x² + x y + 8x + 8y
(ii) 15 xy – 6x + 5y – 2
(iii) ax + bx – ay – by
(iv) 15 pq + 15 + 9q + 25p
(v) z – 7 + 7 x y – x y z
Answer
1) x² + x y + 8x + 8y
= x(x+y) + 8(x+y)
=(x+y)(x+8)
2) 15 xy – 6x + 5y – 2
= 3x(5y-2) +1(5y-2)
=(3x+1)(5y-2)
3) ax + bx – ay – by
= x(a+b) –y(a+b)
=(a+b)(x-y)
4) 15 pq + 15 + 9q + 25p
=15pq+9q +25p+15
= 3q(5p+3) + 5(5p+3)
=(3q+5)(5p+3)
5) z – 7 + 7 x y – x y z
=z-xyz-7+7xy
=z(1-xy)-7(1-xy)
=(z-7)(1-xy)

Download NCERT solutions Factorization Exercise 14.1 as pdf
link to this page by copying the following text


Class 8 Maths Class 8 Science
Reference Books for class 8 Math

Given below are the links of some of the reference books for class 8 Math.

  1. Mathematics Foundation Course for JEE/Olympiad : Class 8 This book can take students maths skills further. Only buy if child is interested in Olympiad/JEE foundation courses.
  2. Mathematics for Class 8 by R S Aggarwal Detailed Mathematics book to clear basics and concepts. I would say it is a must have book for class 8 student.
  3. Pearson Foundation Series (IIT -JEE / NEET) Physics, Chemistry, Maths & Biology for Class 8 (Main Books) | PCMB Combo : These set of books could help your child if he aims to get extra knowledge of science and maths. These would be helpful if child wants to prepare for competitive exams like JEE/NEET. Only buy if you can provide help to the child while studying.
  4. Reasoning Olympiad Workbook - Class 8 :- Reasoning helps sharpen the mind of child. I would recommend students practicing reasoning even though they are not appearing for Olympiad.

You can use above books for extra knowledge and practicing different questions.







Note to our visitors :-

Thanks for visiting our website.
DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. PLEASE READ MY DISCLOSURE FOR MORE INFO.