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WAEC Further Mathematics 2016 Paper

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Question : 16

Total: 40

Find the fourth term in the expansion of

(3x - y)^{6}

.

$-540x^{3}y^{3}$
$-540x^{4}y^{2}$
$-27x^{3}y^{3}$
$540x^{4}y^{2}$

Solution:

Concept:

Use the binomial general term: in

(a+b)^n

, the

(r+1)

th term is

{}^{n}C_{r} a^{n-r} b^{r}

.

Explanation:

Here,

a = 3x

,

b = -y

, and

n = 6

.

The fourth term means

r = 3

.

So the fourth term is:

T_4 = {}^{6}C_{3}(3x)^{6-3}(-y)^{3}

= 20 \times (3x)^3 \times (-y)^3

= 20 \times 27x^3 \times (-y^3)

= -540x^3y^3

Answer:

The fourth term is

-540x^3y^3

, which is Option A.

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