Factorise the following using appropriate identities:
(i) 9x 2 + 6xy + y 2
(ii) 4y 2 – 4y + 1
(iii) x 2 – \(\frac{y^2 }{ 100}\)
Factorise the following using appropriate identities:
(i) 9x 2 + 6xy + y 2
(ii) 4y 2 – 4y + 1
(iii) x 2 – \(\frac{y^2 }{ 100}\)
Solution and Explanation
(i) 9x2 + 6xy + y2 = (3x)2 + 2(3x)(y)+(y)2
= (3x + y)(3x + y) [x2 + 2xy + y2 = (x + y)2]
(ii) 4y2 - 4y + 1 = (2y)2 - 2(2y)91) + (1)2
= (2y - 1)(2y - 1) [x2 - 2xy + y2 = (x - y)2]
(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)]
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