Find the 3rd term of ≤ft(x/2 - 1)^{8} in descending order of x.

Correct Answer is : 7x6167x^6/16167x6

Correct Answer is : 7x6167x^6/16167x6

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WAEC Further Mathematics 2015 Paper

Question : 5

Total: 40

\left(\frac{x}{2} - 1\right)^{8}

in descending order of x.

Solution:

Concept:

Use the binomial theorem to identify the term containing

x^6

in the descending power expansion.

Explanation:

Write

\left(\frac{x}{2} - 1\right)^8

\left(\frac{x}{2} + (-1)\right)^8

The general term in descending powers of

x

is:

T_{r+1} = \binom{8}{r}\left(\frac{x}{2}\right)^{8-r}(-1)^r.

The 3rd term has

r = 2

because

r = 0

gives the first term.

So,

T_3 = \binom{8}{2}\left(\frac{x}{2}\right)^6(-1)^2.

Now evaluate each part:

\binom{8}{2} = 28, \quad \left(\frac{x}{2}\right)^6 = \frac{x^6}{64}, \quad (-1)^2 = 1.

Therefore,

T_3 = 28 \times \frac{x^6}{64} \times 1 = \frac{28x^6}{64} = \frac{7x^6}{16}.

Answer:

\frac{7x^6}{16}

So the correct option is B.

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