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Question

Which of the following operations could make the expression x2+8x3 a perfect square?

A
Add (83)2
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B
Add (43)2
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C
Add (83x)2
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D
Subtract 8x3
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Solution

The correct options are
B Add (43)2
D Subtract 8x3
For making this expression a perfect square,
x2+8x3=x2+2×43×x

(here the (43)2 term is missing which is required to make the expression a perfect square)

So, We should add (43)2
x2+2×43×x+(43)2
(x+43)2
So, if the term (43)2 is added, the expression x2+8x3 becomes a perfect square.

Alternatively we can make the expression equal to x2 by subtracting the expression
8x3.

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