Determine the coefficient of x² in the expansion of (a + 3x)^{6}.

Correct Answer is : 135a4135a^{4}135a4

Correct Answer is : 135a4135a^{4}135a4

Test Index

WAEC Further Mathematics 2011 Paper

Question : 23

Total: 40

x^{2}

(a + 3x)^{6}

Solution:

Concept:

Use the binomial theorem to find the general term of

(a + 3x)^6

Explanation:

The general term in

(a + 3x)^6

is:

T_{r+1} = {}^{6}C_{r} \, a^{6-r} \, (3x)^r

For the term containing

x^2

, set

r = 2

T_{3} = {}^{6}C_{2} \, a^{6-2} \, (3x)^2

= {}^{6}C_{2} \, a^{4} \cdot 9x^2

Now compute the binomial coefficient:

{}^{6}C_{2} = \frac{6!}{2! \, 4!} = 15

Therefore, the coefficient of

x^2

is:

15 \times 9a^4 = 135a^4

Answer:

135a^4

Go to Question:

Prev Question

Next Question