# matix bimonals

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Introduction

Mathematics Portfolio – Matrix Binomials Samed Nakhla

## Matrix Binomials

Question

- Let

Solution

Question

- By considering integer powers of X and Y, find expressions for

Following the pattern in the first question and noticing from it, I deduce that the formula for:

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

Middle

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

Conclusion

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:

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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