Q.3. Factorise the following using appropriate identities:

(i) 9x2 + 6xy + y(ii) 4y2 - 4y + 1  (iii) x- $\frac{{\mathrm{y}}^{2}}{100}$

Solution:

(i) Using identity, (a + b)2 = a2 + 2ab + b2

9x2 + 6xy + y= (3x) 2 + (2×3x×y) + y2

= (3x + y)= (3x + y) (3x + y)

(ii) Using identity, (a - b)2 = a2 - 2ab + b2

4y2 - 4y + 1 = (2y)2 - (2×2y×1) + 12

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

(iii) Using identity, a2 - b2 = (a + b) (a - b)

x- $\frac{{\mathrm{y}}^{2}}{100}$ = x- ${\left(\frac{\mathrm{y}}{10}\right)}^{2}$

= (x - $\frac{\mathrm{y}}{10}$) (x + $\frac{\mathrm{y}}{10}$)