### All SAT Math Resources

## Example Questions

### Example Question #14 : Polynomial Operations

and

What is ?

**Possible Answers:**

**Correct answer:**

so we multiply the two function to get the answer. We use

### Example Question #11 : Polynomial Operations

Find the product:

**Possible Answers:**

**Correct answer:**

Find the product:

Step 1: Use the distributive property.

Step 2: Combine like terms.

### Example Question #16 : Polynomial Operations

represents a positive quantity; represents a negative quantity.

Evaluate

**Possible Answers:**

The correct answer is not among the other choices.

**Correct answer:**

The first two binomials are the difference and the sum of the same two expressions, which, when multiplied, yield the difference of their squares:

Again, a sum is multiplied by a difference to yield a difference of squares, which by the Power of a Power Property, is equal to:

, so by the Power of a Power Property,

Also, , so we can now substitute accordingly:

Note that the signs of and are actually irrelevant to the problem.

### Example Question #17 : Polynomial Operations

represents a positive quantity; represents a negative quantity.

Evaluate .

**Possible Answers:**

**Correct answer:**

can be recognized as the pattern conforming to that of the difference of two perfect cubes:

Additionally, by way of the Power of a Power Property,

, making a square root of , or 625; since is positive, so is , so

.

Similarly, is a square root of , or 64; since is negative, so is (as an odd power of a negative number is negative), so

.

Therefore, substituting:

.

### Example Question #11 : Polynomial Operations

and represent positive quantities.

Evaluate .

**Possible Answers:**

**Correct answer:**

can be recognized as the pattern conforming to that of the difference of two perfect cubes:

Additionally,

and is positive, so

Using the product of radicals property, we see that

and

and is positive, so

,

and

Substituting for and , then collecting the like radicals,

.

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