SOLUTION: (5x^2-1)^2

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Question 185543: (5x^2-1)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%285x%5E2-1%29%5E2 Start with the given expression.


%285x%5E2-1%29%285x%5E2-1%29 Expand. Remember something like A%5E2=A%2AA.


Now let's FOIL the expression.


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


%28highlight%285x%5E2%29-1%29%28highlight%285x%5E2%29-1%29 Multiply the First terms:%285%2Ax%5E2%29%2A%285%2Ax%5E2%29=25%2Ax%5E4.


%28highlight%285x%5E2%29-1%29%285x%5E2%2Bhighlight%28-1%29%29 Multiply the Outer terms:%285%2Ax%5E2%29%2A%28-1%29=-5%2Ax%5E2.


%285x%5E2%2Bhighlight%28-1%29%29%28highlight%285x%5E2%29-1%29 Multiply the Inner terms:%28-1%29%2A%285%2Ax%5E2%29=-5%2Ax%5E2.


%285x%5E2%2Bhighlight%28-1%29%29%285x%5E2%2Bhighlight%28-1%29%29 Multiply the Last terms:%28-1%29%2A%28-1%29=1.


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So we have the terms: 25%2Ax%5E4, -5%2Ax%5E2, -5%2Ax%5E2, and 1


25%2Ax%5E4-5%2Ax%5E2-5%2Ax%5E2%2B1 Now add every term listed above to make a single expression.


25%2Ax%5E4-10%2Ax%5E2%2B1 Now combine like terms.


So %285x%5E2-1%29%5E2 FOILs to 25%2Ax%5E4-10%2Ax%5E2%2B1.


In other words, %285x%5E2-1%29%5E2=25%2Ax%5E4-10%2Ax%5E2%2B1.