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Question

In the expansion of (2x28)(x4)2; find

Coefficient of x3 .

A
26
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B
9
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C
1
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D
16
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Solution

(2x28)(x4)2
=(2x28)(x22x(4)+42) [Since, (ab)2=a22ab+b2]
=(2x28)(x28x+16)

=(2x2×x2)(2x2×8x)+(2x2×16)(8×x2)+(8×8x)(8×16)

=2x416x3+32x28x2+64x128 [Since, am×an=am+n]
=2x416x3+24x2+64x128
Coefficient of x3 is 16

Hence, Option D is correct.


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