Fewpal
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Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.

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+5 votes
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Best answer

Solution:

Using Binomial Theorem, the expressions, (1 + 2x )and (1 – x ), can be expanded as

The complete multiplication of the two brackets is not required to be carried out. Only those terms, which involve x , are required.

Thus, the coefficient of x in the given product is 171.

+2 votes
by (54k points)

Coefficient of x5 in the product of (1+2x)6 (1−x)7

(1+2x)6 (1−x) 7

Expanding using Binomial theorem

Now, the coefficient of xin the product is 

=1×(−21)+12×35+60×(−35)+160×21+240×(−7)+192×1

=−21+420−2100+3360−1680+192

=171

The coefficient of x5 is 171.

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