matix bimonals

Also to find the  power of (X+Y) I will use some examples to find the pattern in it:

From the examples above, I deduced the equation of  by following the pattern, and it is:

Question

Let A=aX and B=bY, where a and b are constants, use different values of a and b to calculate

Solution

First we need to find A, B:

Find  using different values of a and b

Let’s assume that a= 2

Also, let’s assume that b=3

To obtain the general formula for  we need to find a formula for  without using different values of a and b, are:

Question

By considering integer powers of A and B, find expressions for

Solution

By following the pattern in the previous question, one can deduce that the formulas are:

And to find the formula for, one should give some examples and work done on it, so the pattern can be traced and noticed:

So, by noticing the pattern in the examples provided above, I conclude that the formula will be:

Question

Now consider  , show that M= A+B, and that 

Solution

This is solved by keeping a and b as constants, but without using number, so it is kind of a general formula.

To make sure of it, an example is giving, where we replace a=2, and b=3

Question

Hence, find the general statement that expresses in terms of aX and bY.

Solution

After following the pattern in the previous question, I concluded the formula of to be:

To obtain the general formula of in terms of aX and bY:

Question

Test the validity of your general statement by using different values of a, b and n.

Solution

Let’s assume that a=2, b=3 and n=3

And by using the formulas we got from before

Where

So, also by assuming the same variables as before a=2, b=3 and n=3, and then replacing them in the equation, we get the exact result as before: