# ISEE Upper Level Math : Variables and Exponents

## Example Questions

### Example Question #7 : How To Multiply Exponential Variables

Exponentiate:

Explanation:

The cube of a sum pattern can be applied here:

### Example Question #8 : How To Multiply Exponential Variables

Write in expanded form:

Explanation:

The cube of a sum pattern can be applied here:

### Example Question #9 : How To Multiply Exponential Variables

Factor completely:

The expression cannot be factored.

The expression cannot be factored.

Explanation:

A trinomial with leading coefficient  can be factored by looking for two integers to fill in the boxes:

.

The numbers should have product 20 and sum . However, all of the possible factor pairs fail:

The polynomial is prime.

### Example Question #10 : How To Multiply Exponential Variables

Factor completely:

Explanation:

can be seen to be a perfect square trinomial by taking the square root of the first and last terms, multiplying their product by 2, then comparing it to the second term:

Therefore,

### Example Question #41 : Variables And Exponents

Fill in the box to form a perfect square trinomial:

Explanation:

To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is 20, by 2, and square the quotient. The result is

### Example Question #42 : Variables And Exponents

Fill in the box to form a perfect square trinomial:

Explanation:

To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is 9, by 2, and square the quotient. The result is

### Example Question #43 : Variables And Exponents

Multiply:

Explanation:

Use the distributive property, then collect like terms:

Multiply:

Explanation:

### Example Question #45 : Variables And Exponents

Simplify:

Explanation:

Use the pattern, substituting .

### Example Question #46 : Variables And Exponents

Write in expanded form.