Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #186 : Distributive Property

Using the grid method, find the product of .

Possible Answers:

Correct answer:

Explanation:

Using the grid method is an alternate way of doing FOIL. This utilizes the "tic tac toe" grid. Upon creating the grid, we need to write in the binomials we were given to multiply. Such is done like so:

Capture

 and  have been written in on the leftmost column and topmost row as separated terms. In order to carry out FOIL, we must now fill in the four remaining boxes. In order to do so, each box will be solved by mutlipyling the term above it in the topmost row by the term next to it in the leftmost column. For example, the top left box will be filled in by multiplying .

Capture2

Using the same principle, the left bottom box will be completed by multiplying , like so:

Capture3

The remaining boxes in the rightmost column may be solved using the same principle that was used to solve for the middle column. The filled out grid will look like this:

Capture4

The problem is nearly done. All that is left for us to do is to write this as a mathematical expression and collect like terms. Completing this step will yield us our final answer. 

Note that this last step only requires the values from the four boxes we solved for.

Example Question #12 : How To Use The Grid Method For Foil

Solve for the product of  using the grid method.

Possible Answers:

Correct answer:

Explanation:

Using the grid method is an alternate way of doing FOIL. This utilizes the "tic tac toe" grid. Upon creating the grid, we need to write in the binomials we were given to multiply. Such is done like so:

Capture

 and  have been written in on the leftmost column and topmost row as separated terms. In order to carry out FOIL, we must now fill in the four remaining boxes. In order to do so, each box will be solved by mutlipyling the term above it in the topmost row by the term next to it in the leftmost column. For example, the top left box will be filled in by multiplying .

Capture2

Using the same principle, the left bottom box will be completed by multiplying , like so:

Capture3

The remaining boxes in the rightmost column may be solved using the same principle that was used to solve for the middle column. The filled out grid will look like this:

Capture4

The problem is nearly done. All that is left for us to do is to write this as a mathematical expression and collect like terms. Completing this step will yield us our final answer. 

Note that this last step only requires the values from the four boxes we solved for.

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