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WAEC Further Mathematics 2023 Paper

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Question : 11

Total: 40

Find the fifth term in the binomial expansion of

(q + x)^7

.

$21q^2x^5$
$21q^4x^3$
$35q^3x^4$
$35q^5x^2$

Solution:

Concept:

The

r

-th term in the expansion of

(a+b)^n

is given by

\binom{n}{r-1}a^{n-(r-1)}b^{r-1}

.

Explanation:

Here,

a = q

,

b = x

,

n = 7

, and we need the fifth term, so

r = 5

.

Thus,

r - 1 = 4

.

So the fifth term is

\binom{7}{4} q^{7-4} x^{4}

.

This simplifies to

\binom{7}{4} q^{3} x^{4}

.

Now,

\binom{7}{4} = 35

.

Therefore, the fifth term is

35q^{3}x^{4}

.

Answer:

35q^{3}x^{4}

, which is Option C.

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