# ISEE Middle Level Quantitative : How to multiply variables

## Example Questions

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### Example Question #31 : Variables

Mulitply:

Explanation:

The FOIL method works nicely here:

### Example Question #32 : Variables

Which quantity is greater?

and are equal

It is not possible to tell from the information given

is greater

is greater

is greater

Explanation:

is the greater amount.

### Example Question #33 : Variables

Which quantity is greater?

is greater

It is not possible to tell from the information given

and are equal

is greater

is greater

Explanation:

is the greater amount.

### Example Question #34 : Variables

Which quantity is greater?

is greater

is greater

It is not possible to tell from the information given

and are equal

and are equal

Explanation:

and are equal.

### Example Question #35 : Variables

Which quantity is greater?

is greater

is greater

and are equal

It is not possible to tell from the information given

is greater

Explanation:

Use the distributive property to expand.

To compare the expressions, we can remove common factors. and are common in both expressions, so they can be removed:

### Example Question #36 : Variables

Which quantity is greater?

and are equal

It is not possible to tell from the information given

is greater

is greater

is greater

Explanation:

Use the distributive property to evaluate and .

Since , we get:

is the greater quantity.

### Example Question #37 : Variables

Which quantity is greater?

It is not possible to tell from the information given

is greater

is greater

and are equal

is greater

Explanation:

Use the distributive property to evaluate each quantity.

and  are common in both expressions, so we can write:

is the greater quantity

### Example Question #38 : Variables

Which quantity is greater?

is greater

It is not possible to tell from the information given

is greater

and are equal

and are equal

Explanation:

and are equal.

### Example Question #39 : Variables

Which quantity is greater?

and are equal

is greater

It is not possible to tell from the information given

is greater

is greater

Explanation:

is the greater amount.

### Example Question #40 : Variables

Which of the following is equivalent to  ?

All four of the expressions given in the other responses are correct.

All four of the expressions given in the other responses are correct.

Explanation:

We demonstrate that all four of the expressions are equivalent to .

By the associative property of multiplication,

and

By combining like terms, and applying the distribution property:

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