SOLUTION: Multiply: (a-2b)(a+2b)

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Question 176960This question is from textbook
: Multiply: (a-2b)(a+2b) This question is from textbook

Found 2 solutions by jim_thompson5910, dini:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28a-2b%29%28a%2B2b%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%28a%29-2b%29%28highlight%28a%29%2B2b%29 Multiply the First terms:%28a%29%2A%28a%29=a%5E2.


%28highlight%28a%29-2b%29%28a%2Bhighlight%282b%29%29 Multiply the Outer terms:%28a%29%2A%282%2Ab%29=2%2Aa%2Ab.


%28a%2Bhighlight%28-2b%29%29%28highlight%28a%29%2B2b%29 Multiply the Inner terms:%28-2%2Ab%29%2A%28a%29=-2%2Aa%2Ab.


%28a%2Bhighlight%28-2b%29%29%28a%2Bhighlight%282b%29%29 Multiply the Last terms:%28-2%2Ab%29%2A%282%2Ab%29=-4%2Ab%5E2.


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a%5E2%2B2%2Aa%2Ab-2%2Aa%2Ab-4%2Ab%5E2 Now collect every term to make a single expression.


a%5E2-4%2Ab%5E2 Now combine like terms.


So %28a-2b%29%28a%2B2b%29 FOILs to a%5E2-4%2Ab%5E2.


In other words, %28a-2b%29%28a%2B2b%29=a%5E2-4%2Ab%5E2.


Note: this problem is an example of the use of difference of squares.

Answer by dini(5) About Me  (Show Source):
You can put this solution on YOUR website!
(a-2b)*(a+2b)
=a^2+2ba-2ba-(2b)^2
=a^2-4b^2