SOLUTION: Factor a) 4x^2 - 4x + 1 - y^2 Can you please help me ? Thanks so much in advance:)

Algebra ->  Graphs -> SOLUTION: Factor a) 4x^2 - 4x + 1 - y^2 Can you please help me ? Thanks so much in advance:)      Log On


   

Question 870177: Factor
a) 4x^2 - 4x + 1 - y^2
Can you please help me ? Thanks so much in advance:)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First factor 4x%5E2+-+4x+%2B+1 to get


4x%5E2+-+4x+%2B+1


4x%5E2+-+2x+-+2x+%2B+1 Note: a*c = 4*1 = 4, the two numbers -2 and -2 multiply to 4 and add to -4, so that's why I broke up -4x into -2x-2x


%284x%5E2+-+2x%29+%2B+%28-2x+%2B+1%29


2x%282x+-+1%29+%2B+%28-2x+%2B+1%29


2x%282x+-+1%29+-+1%282x+-+1%29


%282x+-+1%29%282x+-+1%29


%282x+-+1%29%5E2


Note: 4x%5E2+-+4x+%2B+1 is a perfect square trinomial, so you can use the special factoring formula for that.


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So


4x%5E2+-+4x+%2B+1+-+y%5E2


turns into


%282x+-+1%29%5E2-y%5E2


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Looking at %282x+-+1%29%5E2-y%5E2 we have a difference of squares. So use the difference of squares factoring formula to go from %282x+-+1%29%5E2-y%5E2 to %282x+-+1-y%29%282x-1%2By%29. You can rearrange things to get %282x-y-1%29%282x%2By-1%29


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The final answer is %282x-y-1%29%282x%2By-1%29