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Question

Factorise the following using appropriate identities: [4 MARKS]
1)9x2+6xy+y2
2)4y24y+1

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Solution

Formula: 1 Mark each
Substitution: 1 Mark
Factorisation: 1 Mark

1) 9x2+6xy+y2

=(3x)2+2(3x)(y)+(y)2......(i)

a2+2ab+b2=(a+b)2
[Comparing equation (i) with the above identity, we get]
a=3x,b=y,

=(3x)2+2(3x)(y)+(y)2=(3x+y)2=(3x+y)(3x+y)


2) 4y24y+1

=(2y)22(2y)(1)+(1)2......(1)

a22ab+b2=(ab)2
Comparing equation(1) with the above identity, we get
a=2y,b=1

=(2y)22(2y)(1)+(1)2=(2y1)2=(2y1)(2y1)

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