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Question

Match the following identities:

A
a29
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B
a2+4a+4
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C
a22a+1
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D
2(a2+1)
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Solution

The correct option is
We know that (x+y)2=x2+y2+2xy
So, (a+2)2=a2+22+2×a×2
=a2+4+4a

We know that (xy)2=x2+y22xy
So, (a1)2=a2+122×a×1
=a2+12a

We know that (x+y)(xy)=x2y2
So, (a+3)(a3)=a232=a29

Similarly, (a+1)2+(a1)2
=a2+1+2a+a2+12a
=2a2+2=2(a2+1)

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