SChand CLASS 9 Chapter 4 Factorisation Exercise 4(F)

 Exercise 4(F)

Question 1

a² + 5a + 6

Sol :

$\begin{aligned} & a^{2}+5 a+6 \\=& a^{2}+2 a+3 a+6\end{aligned}$

=a(a+2)+3(a+2)

=(a+2)(a+3)

Question 2

a² + 6a + 8

Sol :

$a^{2}+6 a+8$

$=a^{2}+2 a+4 a+8$

=a(a+2)+4(a+2)

=(a+4)(a+2)

Question 3

p² + 10p + 16

Sol :

$=p^{2}+10 p+16$

$=p^{2}+2 p+8 p+16$

=p(p+2)+8(p+2)

=(p+2)(p+8)

Question 4

a² + 13a + 42

Sol :

$=a^{2}+13 a+42$

$=a^{2}+7 a+6 a+42$

=a(a+7)+6(a+7)

=(a+6)(a+7)

Question 5

a² + 25a – 54

Sol :

$=a^{2}+25 a-54$

$=a^{2}+27 a-2 a-54$

=a(a+27)-2(a+27)

=(a+27)(a-2)

Question 6

x² + 5x – 176

Sol :

$\begin{aligned} & x^{2}+5 x-176 \\=& x^{2}+16 x-11 x-176 \\=& x(x+16)-11(x+16) \\=&(x+16)(x-11) \end{aligned}$

Question 7

y² – 18y + 65

Sol :

$\begin{aligned} & y^{2}-18 y+65 \\=& y^{2}-13 y-5 y+65 \\=& y(y-13)-5(y-13) \\=&(y-13)(y-5) \end{aligned}$

Question 8

m² – 29m + 204

Sol :

$=m^{2}-29 m+204$

$=m^{2}-17 a-12 m+204$

=m(m-17)-12(m-17)

=(m-17)(m-12)

Question 9

b² – 2b – 48

Sol :

$\begin{aligned} & b^{2}-2 b-48 \\=& b^{2}-8 b+6 b-48 \\=& b(b-8)+6(b-8) \\=&(b+6)(b-8) \end{aligned}$

Question 10

x² – 11x – 102

Sol :

$\begin{aligned} & x^{2}-11 x-102 \\=& x^{2}-17 x+6 x-102 \\=& x(x-17)+6(x-17) \\=&(x+6)(x-17) \end{aligned}$

Question 11

3 – 4t + t²

Sol :

$\begin{aligned} & 3-4 t+t^{2} \\=& 3-3 t-t+t^{2} \\=& 3(1-t)-t(1-t) \\=&(3-t)(1-t) \end{aligned}$

Question 12

51 – 20k + k²

Sol :

$\begin{aligned} & 51-20 k+k^{2} \\=& 51-17 k-3 k+k^{2} \\=& 17(3-k)-k(3-k) \\=&(17-k)(3-k) \end{aligned}$

Question 13

2x² – 10x + 12

Sol :

$2 x^{2}-10 x+12$

$=2\left(x^{2}-5 x+6\right)$

$=2\left[x^{2}-2 x-3 x+6\right)$

=2[x(x-2)-3(x-2)]

=2(x-2)(x-3)

Question 14

3x³ – 33x² + 84x

Sol :

$\begin{aligned} & 3 x^{3}-33 x^{2}+84 x \\=& 3 x\left[x^{2}-11 x+28\right] \\=& 3 x\left[x^{2}-7 x-4 x+28\right] \\=& 3 x[x(x-7)-4(x-7)] \\=& 3 x(x-7)(x-4) \end{aligned}$

Question 15

5y² – 45y – 110

Sol :

$\begin{aligned} & 5 y^{2}-45 y-110 \\=& 5\left(y^{2}-9 y-22\right) \\=& 5\left(y^{2}-11 y+2 y-22\right] \\=& 5[y(y-11)+2(y-11)] \\=& 5(y-11)(y+2) \end{aligned}$

Question 16

$x^{4}-13 x^{2}+36$

Sol :

$x^{4}-13 x^{2}+36$

$x^{4}-13 x^{2}+36$

$=x^{4}-9 x^{2}-4 x^{2}+36$

$=x^{2}\left(x^{2}-9\right)-4\left(x^{2}-9\right)$

$=\left(x^{2}-9\right)\left(x^{2}-4\right)$

$=\left[(x)^{2}-(3)^{2}\right]\left[(x)^{2}-(2)^{2}\right]$

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

Question 17

x² + 3xy – 88y²

Sol :

$=x^{2}+3 x y-88 y^{2}$

$=x^{2}+11 x y-8 x y-88 y^{2}$

$=x(x+11 y)-8 y(x+11 y)$

$=(x+11 y)(x-8 y)$

Question 18

 $x^{4}-x^{2} y^{2}-72 y^{4}$

Sol :

$\begin{aligned} & x^{4}-x^{2} y^{2}-72 y^{4} \\=& x^{4}-9 x^{2} y^{2}+8 x^{2} y^{2}-72 y^{4} \\=& x^{2}\left(x^{2}-9 y^{2}\right)+8 y^{2}\left(x^{2}-9 y^{2}\right) \\=&\left(x^{2}-9 y^{2}\right)\left(x^{2}+8 y^{2}\right) \\=&\left(x^{2}+8 y^{2}\right)\left[(x)^{2}-(3 y)^{2}\right] \\=&\left(x^{2}+8 y^{2}\right)(x-3 y)(x+3 y) \end{aligned}$

Question 19

a³b³ – 9a²b² + 20ab

Sol :

$\begin{aligned} \text { 9. } & a^{3} b^{3}-9 a^{2} b^{2}+20 a b \\ & a^{3} b^{3}-9 a^{2} b^{2}+20 a b \\=& a b\left[a^{2} b^{2}-9 a b+20\right] \\=& a b\left[a^{2} b^{2}-4 a b-5 a b+20\right] \\=& a b[a b(a b-u)-s(a b-4)] \\=& a b(a b-4)(a b-5) \end{aligned}$

Question 20

(x² + x)² + 4 (x² + x) – 21

Sol :

$\left(x^{2}+x\right)^{2}+4\left(x^{2}+x\right)-21$

Let $x^{2}+x=a$, then,

$=a^{2}+4 a-21$

$=a^{2}+7 a-3 a-21$

$=a(a-7)-3(a+7)$

$=(a-3)(a+7)$

$=\left(x^{2}+x-3\right)\left(x^{2}+x+7\right)$