Marianne S.

asked • 05/07/16

(5x^2)-(2x-3)^2

Question from NY State Regents Algebra I exam, #10. (January 2016)   I am having trouble understanding why the answer is #3. 

If anyone can explain it, I would be most appreciative.
 

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Michael F. answered • 05/07/16

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5x2-(2x-3)2=5x2-(4x2-12x+9)=5x2-4x2+12x-9=x2+12x-9
That's as far as I can go without seeing the choices
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Marianne S.

Michael:

Yes, the answer is:  x^2+12X-9!
 
The confusing part to me is 5X^2 - (4x^2-12x+9) -- what is the principle that results in the the -12x+9 to end up being +12x-9?
I, selected the answer X^2-12X+9, which as you point out is wrong.  That's the concept I'm blanking out on.
 
Thanks,
Marianne
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05/07/16

Arthur D.

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Marianne,
               Subtracting a number is the same as adding its opposite.
-(-12x+9)=-(-12x)+(-9)=
the opposite of -12x is 12x
+(-9)=-9 because the opposite of 9 is -9
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05/07/16

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