SOLUTION: Multiply. (5a – 3b)2

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Question 177430: Multiply. (5a – 3b)2
Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
this is just the distributive property in action
:
a(b+c)=ab+ac
:
2(5a-3b)
:
2(5a)+2(-3b)=)=highlight%2810a-6b%29

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

%285a-3b%29%5E2 Start with the given expression.


%285a-3b%29%285a-3b%29 Expand. Remember something like x%5E2=x%2Ax.


Now let's FOIL the expression.


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


%28highlight%285a%29-3b%29%28highlight%285a%29-3b%29 Multiply the First terms:%285%2Aa%29%2A%285%2Aa%29=25%2Aa%5E2.


%28highlight%285a%29-3b%29%285a%2Bhighlight%28-3b%29%29 Multiply the Outer terms:%285%2Aa%29%2A%28-3%2Ab%29=-15%2Aa%2Ab.


%285a%2Bhighlight%28-3b%29%29%28highlight%285a%29-3b%29 Multiply the Inner terms:%28-3%2Ab%29%2A%285%2Aa%29=-15%2Aa%2Ab.


%285a%2Bhighlight%28-3b%29%29%285a%2Bhighlight%28-3b%29%29 Multiply the Last terms:%28-3%2Ab%29%2A%28-3%2Ab%29=9%2Ab%5E2.


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25%2Aa%5E2-15%2Aa%2Ab-15%2Aa%2Ab%2B9%2Ab%5E2 Now collect every term to make a single expression.


25%2Aa%5E2-30%2Aa%2Ab%2B9%2Ab%5E2 Now combine like terms.


So %285a-3b%29%5E2 FOILs to 25%2Aa%5E2-30%2Aa%2Ab%2B9%2Ab%5E2.


In other words, %285a-3b%29%5E2=25%2Aa%5E2-30%2Aa%2Ab%2B9%2Ab%5E2.