SChand CLASS 9 Chapter 4 Factorisation Exercise 4(C)

 Exercise 4(C)

Question 1

x² + 4x + 4

Sol :

$\begin{aligned} & =x^{2}+4 x+4 \\=&(x)^{2}+2 x x \times 2+(2)^{2} \\=&(x+2)^{2} \end{aligned}$

Question 2

x² + 6x + 9

Sol :

$\begin{aligned} & =x^{2}+6 x+9 \\=&(x)^{2}+2 \times x+8+(3)^{2} \\=&(x+3)^{2} \end{aligned}$

Question 3

x² – 10x + 25

Sol :

$\begin{aligned} =&x^{2}-10 x+25 \\ =&\left(x^{2}\right)-2 \times x \times 5+(5)^{2} \\=&(x-5)^{2} \end{aligned}$

Question 4

4x² – 4x + 1

Sol :

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

Question 5

1 – 8x + 16x²

Sol :

$\begin{aligned} =&1-8x+16 x^{2} \\=&(1)^{2}-2 \times 1 \times 4 x+(4 x)^{2} \\=&(1-4 x)^{2} \end{aligned}$

Question 6

$49 x^{4}+168 x^{2} y^{2}+144 y^{4}$

Sol :

$=49 x^{4}+168 x^{2} y^{2}+144 y^{4}$

$\left(7 x^{2}\right)^{2}+2 \times 7 x^{2}+12 y^{2}+\left(12 y^{2}\right)^{2}$

$=\left(7 x^{2}+12 y^{2}\right)^{2}$

Question 7

$x^{2}+x+\frac{1}{4}$

Sol :

$\begin{aligned} =& x^{2}+x+\frac{1}{4} \\=&(x)^{2}(x)^{2}+2 \times x \times 1 / 2+(1 / 2)^{2} \\=&\left(x+\frac{1}{2}\right)^{2} \end{aligned}$

Question 8

$25 p^{2}+\frac{5 p}{2 q}+\frac{1}{16 q^{2}}$

Sol :

$=25 p^{2}+\frac{5 p}{2 q}+\frac{1}{16 q^{2}}$

$=(5 p)^{2}+2 \times 5 p\times \frac{1}{4 q} +\left(\frac{1}{4 q}\right)^{2}$

$=\left(5 p+\frac{1}{4 q}\right)^{2}$