Question 3
Factorise the following using appropriate identities:
(i) $9 x^{2} + 6 x y + y^{2}$
(ii) $4 y^{2} - 4 y + 1$
(iii) $x^{2} - \frac{y^{2}}{100}$

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Solution

(i) $9 x^{2} + 6 x y + y^{2} = (3 x)^{2} + 2 (3 x) y + (y)^{2} = (3 x + y)^{2} [U s i n g a^{2} + 2 a b + b^{2} = (a + b)^{2}] = (3 x + y) (3 x + y)$
(ii) $4 y^{2} - 4 y + 1 = (2 y^{2}) - 2 (2 y) (1) + (1)^{2} = (2 y - 1)^{2} = (2 y - 1) (2 y - 1) [U s i n g a^{2} - 2 a b + b^{2} = (a - b)^{2}]$
(iii) $x^{2} - \frac{y^{2}}{100} = x^{2} - {(\frac{y}{10})}^{2} = (x + \frac{y}{10}) (x - \frac{y}{10}) [U s i n g a^{2} - b^{2} = (a + b) (a - b)]$

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Similar questions

Factorise the following using appropriate identities:

(i) 9x² + 6xy + y²

(ii)

(iii)

9 x^{2} + 6 x y + y^{2}

4 y^{2} - 4 y + 1

x^{2} - \frac{y^{2}}{100}

9 x^{2} + 6 x y + y^{2}

\frac{x^{2}}{4 y^{2}} - \frac{1}{3} + \frac{y^{2}}{9 x^{2}}

4 y^{2} - 4 y + 1

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