### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Use Foil With Exponents

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

**Possible Answers:**

**Correct answer:**

Take the square root of both sides.

Add 3 to both sides of each equation.

### Example Question #2 : How To Use Foil With Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

= *x*^{3}*y*^{3}*z*^{3} + *x*^{2}*y* + *x*^{0}*y*^{0} + *x*^{2}*y*

= *x*^{3}*y*^{3}*z*^{3} + *x*^{2}*y* + 1 + *x*^{2}*y*

= *x*^{3}*y*^{3}*z*^{3} + 2*x*^{2}*y* + 1

### Example Question #3 : How To Use Foil With Exponents

**Possible Answers:**

**Correct answer:**

Use the FOIL method to find the product. Remember to add the exponents when multiplying.

First:

Outside:

Inside:

Last:

Add all the terms:

### Example Question #2 : How To Use Foil With Exponents

Square the binomial.

**Possible Answers:**

**Correct answer:**

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)^{3 }– 8c^{3}d + 2(cd)^{4}?

**Possible Answers:**

cd(54c * d^{3 }– 4c^{3 }+ c^{2 }* d^{2})

2(54d^{2 }– 4c^{2 }+ 2c^{3 }* d^{3})

2cd(54d^{2} – 4c^{2 }+ c^{3 }* d^{3})

None of the other answers

**Correct answer:**

2cd(54d^{2} – 4c^{2 }+ c^{3 }* d^{3})

First calculate each section to yield 4c(27d^{3}) – 8c^{3}d + 2c^{4}d^{4 }= 108cd^{3 }– 8c^{3}d + 2c^{4}d^{4}. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get: 2cd(54d^{2 }– 4c^{2 }+ c^{3}d^{3}).

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