SChand CLASS 9 Chapter 4 Factorisation Exercise 4(G)

 Exercise 4(G)

Question 1

2x² + 3x + 1

Sol :

$\begin{aligned} =& 2 x^{2}+3 x+2 \\=& 2 x^{2}+2 x+x+1 \\=& 2 x(x+2)+1(x+1) \\=&(x+1)(2 x+1) \end{aligned}$

Question 2

3x² + 17x + 10

Sol :

$=3 x^{2}+17 x+20$

$=3 x^{2}+15 x+2 x+20$

$=3 x(x+5)+2(x+5)$

$=(x+5)(3 x+2)$

Question 3

5x² + 9x – 2

Sol :

$\begin{aligned} =& 5 x^{2}+9 x-2 \\=& 5 x^{2}+10 x-x-2 \\=& 5 x(x+2)-1(x+2) \\=&(x+2)(5 x-2) \end{aligned}$

Question 4

6x² – 7x – 5

Sol :

$\begin{aligned} =& 6 x^{2}-7 x-5 \\=& 6 x^{2}-10 x+3 x-5 \\=& 2 x(3 x-5)+1(3 x-5) \\=&(3 x-5)(2 x+1) \end{aligned}$

Question 5

6y² – 17y + 12

Sol :

$\begin{aligned} =& 6 y^{2}-17 y+12 \\=& 6 y^{2}-9 y-8 y+12 \\=& 3 y(2 y-3)-4(2 y-3) \\=&(2 y-3)(3 y-4) \end{aligned}$

Question 6

8y² – 2y – 1

Sol :

$=8 y^{2}-2 y-1$

$=8 y^{2}-4 y+2 y-1$

$=4 y(2 y-1)+1(2 y-2)$

$=(2 y-1)(4 y+2)$

Question 7

18bx² + 18bx – 20b

Sol :

$=18 b x^{2}+18 b x-20 b$

$=2 b\left(9 x^{2}+9 x-20\right)$

$=2 b\left(9 x^{2}+15 x-6 x-10\right)$

$=2 b[3 x(3 x+5)-2(3 x+5)]$

$=2 b(3 x+5)(3 x-2)$

Question 8

14x² – 60xy + 16y²

Sol :

$\begin{aligned} =& 14 x^{2}-60 x y+16 y^{2} \\=& 2\left[7 x^{2}-302 y+8 y^{2}\right] \\=& 2\left[7 x^{2}-28 x y-2 x y+8 y^{2}\right] \\=& 2[7 x(x-4 y)-2 y(x-4 y)] \\=& 2(x-4 y)(7 x-2 y) \end{aligned}$

Question 9

30x² + 103xy – 7y²

Sol :

$\begin{aligned} =& 30 x^{2}+103 x y-7 y^{2} \\=& 30 x^{2}+205 x y-2 x y-7 y^{2} \\=& 15 x(2 x+7 y)-y(2 x-7 y) \\=&(15 x-y)(2 x+7 y) \end{aligned}$

Question 10

12x² – 29xy + 14y²

Sol :

$\begin{aligned} =& 12 x^{2}-29 x y+14 y^{2} \\=& 12 x^{2}-8 x y-21 x y+14 y^{2} \\=& 4 x(3 x-2 y)-7 y(3 x-2 y) \\=&(3 x-2 y)(4 x-7 y) \end{aligned}$

Question 11

15 + p (7 – 2p)

Sol :

$\begin{aligned} =& 15+p(7-2 p) \\=& 15+7 p-2 p^{2} \\=& 15+10 p-3 p-2 p^{2} \\=& 5(3+2 p)-p(3+2 p) \\=&(3+2 p)(5-p) \end{aligned}$

Question 12

2 – y(7 – 5y)

Sol :

$=2-y(7-5 y)$

$=2-7 y+5 y^{2}$

$=2-5 y-2 y+5 y^{2}$

=1(2-5y)-y(2+5y)

=(2-5y)(1-y)

Question 13

x(2x + 5) – 3

Sol :

=x(2 x+5)-3

$=2 x^{2}+5 x-3$

$=2 x^{2}+6 x-x-3$

=2x(x+3)-1(x+3)

=(x+3)(2x-1)

Question 14

1 – 18y – 63y²

Sol :

$\begin{aligned} =& 1-18 y-63 y^{2} \\=& 1-21 y+3y-63 y^{2} \\=& 1(1-21 y)+3 y(y-21 y) \\=&(2-21 y)(1+3 y) \end{aligned}$

Question 15

8a³b – 10a²b² – 12ab³

Sol :

$\begin{aligned} =& 8 a^{3} b-10 a^{2} b^{2}-12 a b^{3} \\=& 2 a b\left(4 a^{2}-5 a b-6 b^{2}\right) \\=& 2 a b\left[4 a^{2}-8 a b+3 a b-6 b^{2}\right] \\=& 2 c b[4 a(a-2 b)+3 b(a-2 b)] \\=& 2 a b(a-2 b)(4 a+3 b) \end{aligned}$

Question 16

2 (a + b)² – 5 (a + b) – 3

Sol :

$=2(a+b)^{2}-5(a+b)-3$

Let a+b=x, then

$\begin{aligned} & 2 x^{2}-5 x-3 \\=& 2 x^{2}-6 x+x-3 \\=& 2 x(x-3)+1(x-3) \\=&(x-3)(2 x+2) \\=&(a+b-3)(2 a+2 b+y) \end{aligned}$