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WAEC Further Mathematics 2017 Paper

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Question : 9

Total: 40

Find the coefficient of

x^{4}

in the expansion of

(1-2x)^{6}

.

-320
-240
240
320

Solution:

Concept:

Use the general term of a binomial expansion to find the coefficient of

x^4

.

Explanation:

The general term in

(1-2x)^6

is:

T_{r+1} = {}^6C_r (1)^{6-r}(-2x)^r

.

Since

1^{6-r} = 1

, this becomes:

T_{r+1} = {}^6C_r (-2)^r x^r

.

To get the term containing

x^4

, set

r = 4

.

T_5 = {}^6C_4 (-2)^4 x^4

.

Now,

{}^6C_4 = 15

and

(-2)^4 = 16

.

So the coefficient is

15 \times 16 = 240

.

The sign is positive because

(-2)^4

is positive.

Answer:

C. 240

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