SAT Math : Exponents and the Distributive Property

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Exponents And The Distributive Property

Factor 2x2 - 5x – 12

Possible Answers:

(x + 4) (2x + 3)

(x + 4) (2x + 3)

(x – 4) (2x – 3)

(x - 4) (2x + 3)

Correct answer:

(x - 4) (2x + 3)

Explanation:

Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.

Example Question #2 : How To Use Foil

x > 0.

Quantity A: (x+3)(x-5)(x)

Quantity B: (x-3)(x-1)(x+3)

Possible Answers:

The relationship cannot be determined from the information given

Quantity A is greater

The two quantities are equal

Quantity B is greater

Correct answer:

Quantity B is greater

Explanation:

 

Use FOIL: 

 

  (x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.

 

  (x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)

  (x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B. 

The difference between A and B: 

 (x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9

 = - x2 - 4x - 9. Since all of the terms are negative and x > 0:

  A - B < 0.

Rearrange A - B < 0:

  A < B

 

 

 

Example Question #1 : Exponents And The Distributive Property

Solve for all real values of .

Possible Answers:

Correct answer:

Explanation:

First, move all terms to one side of the equation to set them equal to zero.

All terms contain an , so we can factor it out of the equation.

Now, we can factor the quadratic in parenthesis. We need two numbers that add to and multiply to .

We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.

Our answer will be .

Example Question #2 : New Sat Math No Calculator

Find the product in terms of :

Possible Answers:

Correct answer:

Explanation:

This question can be solved using the FOIL method. So the first terms are multiplied together:

This gives:

The x-squared is due to the x times x. 

The outer terms are then multipled together and added to the value above. 

The inner two terms are multipled together to give the next term of the expression.

Finally the last terms are multiplied together.

All of the above terms are added together to give:

Combining like terms gives

.

Example Question #1 : Exponents And The Distributive Property

Expand the following expression:

Possible Answers:

Correct answer:

Explanation:

Expand the following expression:

Let's begin by recalling the meaning of FOIL: First, Outer, Inner, Last.

This means that in a situation such as we are given here, we need to multiply all the terms in a particular way. FOIL makes it easy to remember to multiply each pair of terms.

Let's begin:

First: 

Outer:

Inner:

Last:

Now, put it together in standard form to get:

Example Question #1 : Exponents And The Distributive Property

If , which of the following could be the value of ?

Possible Answers:

Correct answer:

Explanation:

Take the square root of both sides.

Add 3 to both sides of each equation.

Example Question #1 : Exponents And The Distributive Property

Simplify:

Possible Answers:

Correct answer:

Explanation:

= x3y3z3 + x2y + x0y0 + x2y

x3y3z3 + x2y + 1 + x2y

x3y3z3 + 2x2y + 1

Example Question #2 : How To Use Foil With Exponents

Use the FOIL method to simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to simplify the following expression:

Step 1: Expand the expression.

Step 2: FOIL

First:

Outside:

Inside:

Last:

Step 2: Sum the products.

Example Question #1 : Exponents And The Distributive Property

Square the binomial.

Possible Answers:

Correct answer:

Explanation:

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

Example Question #1 : Exponents And The Distributive Property

Which of the following is equivalent to 4c(3d)– 8c3d + 2(cd)4?

Possible Answers:

2cd(54d2 – 4c+ c* d3)

cd(54c * d– 4c+ c* d2)

2(54d– 4c+ 2c* d3)

None of the other answers

Correct answer:

2cd(54d2 – 4c+ c* d3)

Explanation:

First calculate each section to yield 4c(27d3) – 8c3d + 2c4d= 108cd– 8c3d + 2c4d4. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get:  2cd(54d– 4c+ c3d3).

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