SOLUTION: How do I multiply {{{(4ab-1)^2}}}, should I multiply it using foil or is there another option?

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Question 118317: How do I multiply %284ab-1%29%5E2, should I multiply it using foil or is there another option?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%284ab-1%29%5E2 Start with the given expression


%284ab-1%29%284ab-1%29 Expand. Something like x%5E2 is the same as x%2Ax

Now let's foil the expression


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


%28highlight%284ab%29-1%29%28highlight%284ab%29-1%29 Multiply the First terms:%284ab%29%2A%284ab%29=16a%5E2b%5E2


%28highlight%284ab%29-1%29%284ab%2Bhighlight%28-1%29%29 Multiply the Outer terms:%284ab%29%2A%28-1%29=-4ab


%284ab%2Bhighlight%28-1%29%29%28highlight%284ab%29-1%29 Multiply the Inner terms:%28-1%29%2A%284ab%29=-4ab


%284ab%2Bhighlight%28-1%29%29%284ab%2Bhighlight%28-1%29%29 Multiply the Last terms:%28-1%29%2A%28-1%29=1


16a%5E2b%5E2-4ab-4ab%2B1 Now collect every term to make a single expression



16a%5E2b%5E2-8ab%2B1 Now combine like terms


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Answer:
So %284ab-1%29%284ab-1%29 foils and simplifies to 16a%5E2b%5E2-8ab%2B1

In other words, %284ab-1%29%284ab-1%29=16a%5E2b%5E2-8ab%2B1


note: there is another way to do this problem, but I'm not sure if your math class has covered it or not.