# SAT Math : How to multiply polynomials

## Example Questions

### Example Question #1 : How To Multiply Polynomials

and

What is ?

Explanation:

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

### Example Question #31 : Variables

Find the product:

Explanation:

Find the product:

Step 1: Use the distributive property.

Step 2: Combine like terms.

### Example Question #3 : How To Multiply Polynomials

represents a positive quantity;  represents a negative quantity.

Evaluate

The correct answer is not among the other choices.

Explanation:

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 #11 : Polynomial Operations

represents a positive quantity;  represents a negative quantity.

Evaluate .

Explanation:

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 #31 : Variables

and  represent positive quantities.

Evaluate .

Explanation:

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

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,

.