Ncert solutions

Ncert solutions

Grade 8

Factorisation | Exercise 14.1

Question 1

Q1) Find the common factors of the given terms.

(i) 12x, 36

(ii) 2y, 22xy

(iii) 14\ pq,\ 28p^2q^2

(iv) 2x,3x^2,\ 4

(v) 6abc,\ 24ab^2,\ 12a^2b

(vi) 16x^3,\ -4x^2,\ 32x

(vii) 10\ pq,\ 20qr,\ 30rp

(viii) 3x^2y^3,\ 10x^3y^2,\ 6x^2y^2z

Solution 1:

(i) 12x\ =\ 12\times x

36\ =\ 12\times3

common factor = 12

(ii) 2y=2\times y

22xy=\ 2\times11\times x\times y

common factor = 2,y

(iii) 14\ pq\ =\ p\times q\times7\times2

28p^2q^2\ =\ 2\times2\times7\times p\times p\times q\times q

Common factor =7\times2\times p\times q\ =14pq

(iv) 2x=\ 2\times x\times1

3\times x\times x\times1

4=\ 2\times2\times1

common factor =1

(v) 6abc\ =\ 2\times3\times a\times b\times c

24\ ab^2\ =\ 2\times3\times4\times a\times b\times b

12a^2b\ =2\times2\times3\times a\times a\times b

Common factor = 2\times3\times a\times b\ =\ 6ab

(vi) 16x^{3\ }=\ 2\times2\times2\times2\times x\times x\times x

-4x^2=\ 2\times2\times x\times x\times\left(-1\right)

32x\ =\ 2\times2\times2\times2\times2\times2\times x

common factor = 2\times2\times x\ =4x

(vii) 10pq=2\times5\times p\times q

20qr\ =\ 2\times2\times5\times q\times r

30rp\ =\ 3\times2\times5\times r\times p

common factor = 2\times5=10

(viii) 3x^2y^2=\ 3\times x\times x\times y\times y\times y

10x^3y^2=\ 2\times5\times x\times x\times x\times y\times y

6x^2y^2z\ =\ 2\times3\times x\times x\times y\times y\times z

common factor = x^2y^2

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Question 1

Q1) Find the common factors of the given terms.

(i) 12x, 36

(ii) 2y, 22xy

(iii) 14\ pq,\ 28p^2q^2

(iv) 2x,3x^2,\ 4

(v) 6abc,\ 24ab^2,\ 12a^2b

(vi) 16x^3,\ -4x^2,\ 32x

(vii) 10\ pq,\ 20qr,\ 30rp

(viii) 3x^2y^3,\ 10x^3y^2,\ 6x^2y^2z

Solution 1:

(i) 12x\ =\ 12\times x

36\ =\ 12\times3

common factor = 12

(ii) 2y=2\times y

22xy=\ 2\times11\times x\times y

common factor = 2,y

(iii) 14\ pq\ =\ p\times q\times7\times2

28p^2q^2\ =\ 2\times2\times7\times p\times p\times q\times q

Common factor =7\times2\times p\times q\ =14pq

(iv) 2x=\ 2\times x\times1

3\times x\times x\times1

4=\ 2\times2\times1

common factor =1

(v) 6abc\ =\ 2\times3\times a\times b\times c

24\ ab^2\ =\ 2\times3\times4\times a\times b\times b

12a^2b\ =2\times2\times3\times a\times a\times b

Common factor = 2\times3\times a\times b\ =\ 6ab

(vi) 16x^{3\ }=\ 2\times2\times2\times2\times x\times x\times x

-4x^2=\ 2\times2\times x\times x\times\left(-1\right)

32x\ =\ 2\times2\times2\times2\times2\times2\times x

common factor = 2\times2\times x\ =4x

(vii) 10pq=2\times5\times p\times q

20qr\ =\ 2\times2\times5\times q\times r

30rp\ =\ 3\times2\times5\times r\times p

common factor = 2\times5=10

(viii) 3x^2y^2=\ 3\times x\times x\times y\times y\times y

10x^3y^2=\ 2\times5\times x\times x\times x\times y\times y

6x^2y^2z\ =\ 2\times3\times x\times x\times y\times y\times z

common factor = x^2y^2

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