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Question

Factorize 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 using a2+2ab+b2=(a+b)2
=(3x+y)2

(ii)4y24y+1=(2y)22×2y×1+12 using a2=2ab+b2=(a+b)2
=(2y1)2

(iii)x2y2100=x2y2102 is of the form a2b2=(a+b)(ab)

=(x+y10)(xy10)

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