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Factorize the following using appropriate identities:

(i). $9 x^{2} + 6 xy + y^{2}$

(ii). $4 y² - 4 y + 1$

(iii). $x^{2} - \frac{y^{2}}{100}$

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(i).

(3 x + y) ²

, (ii)

(2 y - 1) ²

,(iii)

(x + \frac{y}{10}) (x - \frac{y}{10})

(i).

(2 x + y)

, (ii).

(2 x + 1)

,(iii)

(x + \frac{y}{10}) (x - \frac{y}{10})

(i)

(4 x + y) ²

, (ii).

(2 y + 1)

, (iii).

(x + \frac{y}{10}) (x + \frac{y}{10})

(i).

(3 x - y) ²

, (ii).

(2 x + 1) ²

, (iii).

(x + \frac{y}{20}) (x - \frac{y}{10})

answer is A.

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Detailed Solution

Concept: Algebraic expressions are (a+b)²= a²+ 2ab+b², (a+b)(a-b)= a²-b².
(i)

9 x² + 6 xy + y²

= 3 x^{2} + 2 (3 x) (y) + y^{2}

Consider,

a = 3 x, b = y

Hence,

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

{(3 x + y)}^{2}

(ii)

4 y² - 4 y + 1

= 2 y^{2} - 2 (2 y) (1) + 1^{2}

Consider,

a = 2 y, b = 1

Hence,

4 y^{2} - 4 y + 1

= {(2 y - 1)}^{2}

(iii)

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

{= x}^{2} - {(\frac{y}{10})}^{2}

Consider,

a = x, b = \frac{y}{10}

Hence,

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

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

Hence, the correct answer is option 1.

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Factorize the following using appropriate identities: (i). 9x2+6xy+ y2 (ii). 4y²-4y+1 (iii).x2-y2100

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Detailed Solution

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Factorize the following using appropriate identities:

(i). $9 x^{2} + 6 xy + y^{2}$

(ii). $4 y² - 4 y + 1$

(iii). $x^{2} - \frac{y^{2}}{100}$