SOLUTION: we are learning how the quadratic formula is derived. There is one small step in process i do not understand. how does {{{(b^2/4a^2)-(c/a)}}} become {{{(b^2-4ac)/4a^2}}} I know

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: we are learning how the quadratic formula is derived. There is one small step in process i do not understand. how does {{{(b^2/4a^2)-(c/a)}}} become {{{(b^2-4ac)/4a^2}}} I know      Log On

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Question 17581: we are learning how the quadratic formula is derived.
There is one small step in process i do not understand.
how does %28b%5E2%2F4a%5E2%29-%28c%2Fa%29 become
%28b%5E2-4ac%29%2F4a%5E2
I know it is very basic but I cannot see how
Thanks
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
%28b%5E2%2F4a%5E2%29-%28c%2Fa%29
The LCM of 4a^2 and a is 4a^2
Then,
%28b%5E2-4ac%29%2F%284a%5E2%29
[to convert a to 4a^2 we need to multiply by '4a',hence the numerator is also multiplied by 4a]


In other form,
%28b%5E2%2F4a%5E2%29-%28%28c%2Fa%29%2A%284a%2F4a%29%29
[Multiplying by 4a/4a is the same as multiplying by one. Hence the fraction does not change.]
%28b%5E2%2F4a%5E2%29-%284ac%2F4a%5E2%29
[Now since the denominators are the same,we can subtract]
%28b%5E2-4ac%29%2F%284a%5E2%29
[And this is our final expression]


Hope this helps,
Prabhat