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Question

Question 3
Factorise the following using appropriate identities:
(i) 9x2+6xy+y2
(ii) 4y24y+1
(iii) x2y2100

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Solution

(i) 9x2+6xy+y2=(3x)2+2(3x)y+(y)2=(3x+y)2 [Using a2+2ab+b2=(a+b)2]=(3x+y)(3x+y)
(ii) 4y24y+1=(2y2)2(2y)(1)+(1)2=(2y1)2=(2y1)(2y1)[Using a22ab+b2=(ab)2]
(iii) x2y2100=x2(y10)2=(x+y10)(xy10) [Using a2b2=(a+b)(ab)]

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