SOLUTION: Using FOIL, multiply the expression (3x+2)(3x-2) Show that a particular factoring formula can be used to get the same answer. Thanks so much! I'm lost again!

Algebra ->  Equations -> SOLUTION: Using FOIL, multiply the expression (3x+2)(3x-2) Show that a particular factoring formula can be used to get the same answer. Thanks so much! I'm lost again!      Log On


   

Question 190672This question is from textbook
: Using FOIL, multiply the expression (3x+2)(3x-2) Show that a particular factoring formula can be used to get the same answer. Thanks so much! I'm lost again! This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283x%2B2%29%283x-2%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%283x%29%2B2%29%28highlight%283x%29-2%29 Multiply the First terms:%283%2Ax%29%2A%283%2Ax%29=9%2Ax%5E2.


%28highlight%283x%29%2B2%29%283x%2Bhighlight%28-2%29%29 Multiply the Outer terms:%283%2Ax%29%2A%28-2%29=-6%2Ax.


%283x%2Bhighlight%282%29%29%28highlight%283x%29-2%29 Multiply the Inner terms:%282%29%2A%283%2Ax%29=6%2Ax.


%283x%2Bhighlight%282%29%29%283x%2Bhighlight%28-2%29%29 Multiply the Last terms:%282%29%2A%28-2%29=-4.


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So we have the terms: 9%2Ax%5E2, -6%2Ax, 6%2Ax, -4


9%2Ax%5E2-6%2Ax%2B6%2Ax-4 Now add every term listed above to make a single expression.


9%2Ax%5E2-4 Now combine like terms.


So %283x%2B2%29%283x-2%29 FOILs to 9%2Ax%5E2-4.


In other words, %283x%2B2%29%283x-2%29=9x%5E2-4.

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Now, let's factor the answer to check our work:


9x%5E2-4 Start with the given expression.


%283x%29%5E2-4 Rewrite 9x%5E2 as %283x%29%5E2.


%283x%29%5E2-%282%29%5E2 Rewrite 4 as %282%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=3x and B=2.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%283x%29%5E2-%282%29%5E2=%283x%2B2%29%283x-2%29 Plug in A=3x and B=2.


So this shows us that 9x%5E2-4 factors to %283x%2B2%29%283x-2%29.


In other words 9x%5E2-4=%283x%2B2%29%283x-2%29.


So this confirms our answer