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)]