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Question

Which of the following operations can
convert the expression (x2+8x3)
into a perfect square?

A
Addition of (83)2.
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B
Addition of (43)2.
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C
Addition of (83x)2.
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D
Subtraction of 8x3
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Solution

The correct option is B Addition of (43)2.
To make x2+8x3a perfect square, divide the co-efficient of x by 2 and the add the square of the result to x2+8x3to convert it into a perfect square.

Adding (83÷2)2=(43)2 to x2+8x3, we have,

x2+8x3+(43)2=x2+2(x)(43)+(43)2=(x+43)2, a perfect square

(Using the identity, (a+b)2=a2+2ab+b2)

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