ISEE Upper Level Math : How to add exponential variables

Example Questions

Example Question #1 : Variables And Exponents

Rewrite the polynomial in standard form:

Explanation:

The degree of a term of a polynomial with one variable is the exponent of that variable. The terms of a polynomial in standard form are written in descending order of degree. Therefore, we rearrange the terms by their exponent, from 5 down to 0, noting that we can rewrite the  and constant terms with exponents 1 and 0, respectively:

Simplify:

Explanation:

Example Question #1 : How To Add Exponential Variables

Assume that . Simplify:

Explanation:

If , simplify:

Explanation:

If , simplify:

Explanation:

Example Question #6 : Variables And Exponents

Define

What is  ?

Explanation:

Substitute  for  in the definition:

Explanation:

Example Question #3 : How To Add Exponential Variables

Simplify:

Explanation:

We can expand the first term using FOIL:

Reorder the expression to group like-terms together.

Simplify by combining like-terms.

Example Question #9 : Variables And Exponents

Simplify:

Explanation:

Expand each term by using FOIL:

Rearrange to group like-terms together.

Simplify by combining like-terms.

Example Question #4 : How To Add Exponential Variables

Simplify:

The expression can not be simplified further