# SAT II Math II : Simplifying Expressions

## Example Questions

### Example Question #1 : Simplifying Expressions

Decrease  by 40%. Which of the following will this be equal to?

Explanation:

A number decreased by 40% is equivalent to 100% of the number minus 40% of the number. This is taking 60% of the number, or, equivalently, multiplying it by 0.6.

Therefore,  decreased by 40% is 0.6 times this, or

Simplify:

Explanation:

### Example Question #1 : Simplifying Expressions

Assume all variables assume positive values.

Simplify:

Explanation:

### Example Question #1 : Simplifying Expressions

Assume all variables assume positive values. Simplify:

The expression is undefined.

Explanation:

Any nonzero expression raised to the power of 0 is equal to 1. Therefore,

### Example Question #1 : Simplifying Expressions

Simplify the following expression:

Explanation:

Distribute the outer term through both terms in the parentheses.

Multiply each term.

There are no like-terms.

### Example Question #2 : Simplifying Expressions

Simplify the expression:

Explanation:

Distribute the integers through the binomials.

Combine like-terms.

### Example Question #3 : Simplifying Expressions

Simplify .

Explanation:

We can start by distributing the negative sign in the parentheses term:

Now we can combine like terms.  The constants go together, and the variables go together:

### Example Question #51 : Single Variable Algebra

Simplify .

Explanation:

First, we can distribute the negative sign through the parentheses term:

Now we gather like terms.  Remember, you can't gather different variables together.  The 's and 's will still be separate terms:

### Example Question #4 : Simplifying Expressions

Simplify .

Explanation:

Start by distributing the negative sign through the parentheses term:

Now combine like terms.  Each variable can't be combined with different variables:

Simplify