Question

Factorise the following using appropriate identities: 

(i) 9x ² + 6xy + y 2 

(ii) 4y ² – 4y + 1 

(iii) x ² – \(\frac{y^2 }{ 100}\)

Answer 1

(i) 9x² + 6xy + y² = (3x)² + 2(3x)(y)+(y⁾² 

= (3x + y)(3x + y)     [x² + 2xy + y² = (x + y)²]

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(ii) 4y² - 4y + 1 = (2y)² - 2(2y)91) + (1)² 

= (2y - 1)(2y - 1)      [x² - 2xy + y² = (x - y)²]

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(iii) x² -\(\frac{y^2 }{ 100}\) = x2 - (\(\frac{y }{ 10}\))² 

= (x + \(\frac{y }{ 10}\)) (x -\(\frac{y }{ 10}\))     [x² - y² = (x + y) (x - y)]