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Question

If a=6p and b=3p, then (a+b)2+(ab)2 = .

A
72p218q2
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B
72p2+18q2
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C
18p2+72q2
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Solution

The correct option is B 72p2+18q2

Given: a=6p and b=3q
To find: (a+b)2+(ab)2

We know that,
(a+b)2=a2+2ab+b2(ab)2=a22ab+b2

(a+b)2+(ab)2=a2+2ab+b2+a22ab+b2=2a2+2b2

On substituting the values of a and b, we get,
(a+b)2+(ab)2=(6p+3q)2+(6p3q)2=2(6p)2+2(3q)2=2(36p2)+2(9q)2=72p2+18q2

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