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Question

Find the value of (A+B)2 given that x4,A2=x2+12x+36 and B2=4x228x+49

A
2x2+5x+42
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B
3x29x1
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C
4x2x+13
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D
5x226x+85
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E
9x26x+1
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Solution

The correct option is E 9x26x+1
A2=x2+12x+36=(x+6)2
A=|x+6|
B2=4x228x+49=(2x7)2
B=|2x7|
AB=|(x+6)(2x7)|=|2x2+5x42|
(A+B)2=A2+B2+2AB
=5x216x+85+|4x2+10x84|
=9x26x+1

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