SOLUTION: what is (3a+b)(2a-5b)

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Question 214131: what is (3a+b)(2a-5b)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283a%2Bb%29%282a-5b%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%283a%29%2Bb%29%28highlight%282a%29-5b%29 Multiply the First terms:%283%2Aa%29%2A%282%2Aa%29=6%2Aa%5E2.


%28highlight%283a%29%2Bb%29%282a%2Bhighlight%28-5b%29%29 Multiply the Outer terms:%283%2Aa%29%2A%28-5%2Ab%29=-15%2Aa%2Ab.


%283a%2Bhighlight%28b%29%29%28highlight%282a%29-5b%29 Multiply the Inner terms:%28b%29%2A%282%2Aa%29=2%2Aa%2Ab.


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


6%2Aa%5E2-15%2Aa%2Ab%2B2%2Aa%2Ab-5%2Ab%5E2 Now collect every term to make a single expression.


6%2Aa%5E2-13%2Aa%2Ab-5%2Ab%5E2 Now combine like terms.


So %283a%2Bb%29%282a-5b%29 FOILs to 6%2Aa%5E2-13%2Aa%2Ab-5%2Ab%5E2.


In other words, %283a%2Bb%29%282a-5b%29=6%2Aa%5E2-13%2Aa%2Ab-5%2Ab%5E2.