Mathematics: If ax7yb is a term from the expansion of (x + y)12, describe how to determine its coefficient a and missing exponent b without writing the entire expansion.

If ax7yb is a term from the expansion of (x +

masonsee4ytube

11.03.2022

ANSWER

a) Use the homogeneous property of the binomial expansion to find the missing exponent

b) Use the binomial theorem to find the coefficient

EXPLANATION

The given binomial expansion is:

$(x+y)^{12}$

When we compare this to

$(a + b) ^{n}$

We have

n = 12

Therefore the of each term in the expansion must be 12.

$\implies \: 7 + b = 12$

b = 12 - 7

b = 5

Since the coefficient of x and y are unity, we use the formula

$^{n} C_r = \frac{n!}{(n - r)!r!}$

to find the coefficient.

Where n=12 and r=5(the exponent of the y-term).

Therefore the coefficient is

$^{12} C_5= \frac{12!}{(12- 5)!5!}$

$^{12} C_5= \frac{12!}{7!5!}$

$^{12} C_5= \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7! \times 5 \times 4 \times 3 \times 2 \times 1}$

When we simplify further we get:

$^{12} C_5= 11 \times 9 \times 8 = 792$

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mayorga2genesis2

28.02.2023

Step-by-step explanation:

39+4+9= -14

39 + 9=48

48 + 4=52

52 - 14=38

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