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 sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: