SAT Math : How to use FOIL in the distributive property

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #921 : Algebra

Simplify: 

Possible Answers:

Correct answer:

Explanation:

Use FOIL:

Example Question #31 : Foil

What is a possible solution for  if the equation has exactly one solution for ?

Given

Possible Answers:

Correct answer:

Explanation:

Given

First FOIL the first equation. FOIL means to multiply each term in the first binomial with each term in the second binomial.

Now solve the second equation for .

Substitute the equation for  into the first equation to get a new equation only in terms of .

Distribute to eliminate the parentheses and simplify.

Now use the quadratic formula.

Given a quadratic in the form, 

 

For this particular question,

From here recall that if the value under the radical sign equals zero than  results in having just one solution.

Therefore, set the value that is under the radical equal to zero and solve for .

Since the binomials containing  are the same, set one equal to zero and solve.

Example Question #32 : How To Use Foil In The Distributive Property

Expand the following expression found below:

Possible Answers:

Correct answer:

Explanation:

If a problem asks you to expand an expression, you must use the Distributive property. If you are using the FOIL method, you first multiply the first term in each parentheses by each other, followed by the outside terms, then the inside terms, and then the last terms. This is illustrated below. 

 Screen shot 2015 10 27 at 1.54.06 pm

First, you multiply  which equals 

Second, you multiply 

Third, you multiply 

Last, you multiply 

Then you simply rearrange them in order of exponents to get 

Example Question #34 : Distributive Property

Define an operation  on the set of real numbers as follows:

For all real ,

How else could this operation be defined?

Possible Answers:

Correct answer:

Explanation:

The problem is basically asking for two binomial expressions to be multiplied and the product to be simplified.

Multiply the two binomials in the definition of the operation using the FOIL method - multiplying each term in the first binomial by each term in the second, as follows:

F(irst): 

O(uter): 

I(nner): 

L(last): 

Add the terms and collect like terms:

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