SOLUTION: (a+2b)(a+3b)

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Question 170773: (a+2b)(a+3b)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28a%2B2b%29%28a%2B3b%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%2B2b%29%28highlight%28a%29%2B3b%29 Multiply the First terms:%28a%29%2A%28a%29=a%5E2.


%28highlight%28a%29%2B2b%29%28a%2Bhighlight%283b%29%29 Multiply the Outer terms:%28a%29%2A%283%2Ab%29=3%2Aa%2Ab.


%28a%2Bhighlight%282b%29%29%28highlight%28a%29%2B3b%29 Multiply the Inner terms:%282%2Ab%29%2A%28a%29=2%2Aa%2Ab.


%28a%2Bhighlight%282b%29%29%28a%2Bhighlight%283b%29%29 Multiply the Last terms:%282%2Ab%29%2A%283%2Ab%29=6%2Ab%5E2.


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a%5E2%2B3%2Aa%2Ab%2B2%2Aa%2Ab%2B6%2Ab%5E2 Now collect every term to make a single expression.


a%5E2%2B5%2Aa%2Ab%2B6%2Ab%5E2 Now combine like terms.


So %28a%2B2b%29%28a%2B3b%29 FOILs to a%5E2%2B5%2Aa%2Ab%2B6%2Ab%5E2.


In other words, %28a%2B2b%29%28a%2B3b%29=a%5E2%2B5%2Aa%2Ab%2B6%2Ab%5E2.