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.

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:

When we compare this to

We have

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

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

to find the coefficient.

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

Therefore the coefficient is

When we simplify further we get:

the amount you'd have after the work is $1.55

step-by-step explanation:

you subtract 95% from $31.

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