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 Posted: Fri Mar 20, 2009 3:41 pm
Sorry, all the twos are supposed to be squares.
Here it is again with the bold and italic numbers are exponents to the number in front of them:
(a2-b2 = a2-ab+ab-b2?
How many of you can get the right answer?
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Posted: Sun Mar 22, 2009 2:26 pm
Hmmm...
(a2-b2)
=
(a x a) - (b x b)
...
a2 - ab + ab - b2
=
a2 -b2
Oh, yes! Of course they are equal. If you are subtracting ab, and then adding ab, then the two cancel out. You get the exact same answer.
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Posted: Sun Mar 22, 2009 11:30 pm
assume a is 3, b is 2.
(a^2-b^2) = a^2-ab+ab-b^2
9-4 = 5; 9 [-6 +6] -4 = 5.
Same.
assume a is the square root of negative 1 (i), b is 1.
i^2 = -1 - [1^2 = 1] = -2.
i^2 = -1 [- 1i + 1i] -1 = -2.
Still same.
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Posted: Sun Apr 05, 2009 8:23 am
I had a test recently on quadratic functions and factoring, and to factor the difference of squares we used this equation.
(a^2 - b^2) = (a + b)(a - b)
If you work it out, the second is the same as the first. I think that's what you're looking for.
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Posted: Sun Apr 05, 2009 8:27 am
Now, what you did was take the initial statement and use the FOIL* distributive technique. You did it correctly, so yes, the two are equal.
*First, Outer, Inner, Last
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Posted: Sun Apr 26, 2009 10:09 am
The FOIL method only works when there's an exponent on the OUTSIDE of the parentheses, that's applied to multiple terms within the parentheses.
(x+y)^2 = x^2+xy+xy+y^2
so for the [removed](a^2-b^2)
FOIL would not apply because there is no exponent outside the parentheses. It's just two squared terms enclosed by a pair of unneccessary parentheses.
However, the expression is factorable because it is a difference of squares binomial.
(a+b)(a-b) = a^2-ab+ab-b^2
plus and minus ab terms cancel out, leaving a^2-b^2
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Posted: Sun May 03, 2009 9:00 pm
OMG WILL U GUYS TEACH ME MATH (im only in 7th grade) YAY I GOT IT RIGHT THO YAY (it was kinda simple) stare
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Posted: Thu May 14, 2009 8:01 pm
Alex Castellan The FOIL method only works when there's an exponent on the OUTSIDE of the parentheses, that's applied to multiple terms within the parentheses. (x+y)^2 = x^2+xy+xy+y^2 so for the [removed](a^2-b^2) FOIL would not apply because there is no exponent outside the parentheses. It's just two squared terms enclosed by a pair of unneccessary parentheses. However, the expression is factorable because it is a difference of squares binomial. (a+b)(a-b) = a^2-ab+ab-b^2 plus and minus ab terms cancel out, leaving a^2-b^2 I don't believe that FOIL applies exclusively to terms with exponents, but just with multiplying any two binomials (If I recall correctly, that would imply something like (a+b)(c+d). If you have a term in parentheses and squared, then that's the same as writing it once and times itself, then FOIL would apply. But you can still use foil with (6+2)(3-7) or something. (6+2)(3-7) +12 -42 +6 -14 = -38 ...Yeah.
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Posted: Sat May 16, 2009 4:25 pm
Jerba2 Alex Castellan The FOIL method only works when there's an exponent on the OUTSIDE of the parentheses, that's applied to multiple terms within the parentheses. (x+y)^2 = x^2+xy+xy+y^2 so for the [removed](a^2-b^2) FOIL would not apply because there is no exponent outside the parentheses. It's just two squared terms enclosed by a pair of unneccessary parentheses. However, the expression is factorable because it is a difference of squares binomial. (a+b)(a-b) = a^2-ab+ab-b^2 plus and minus ab terms cancel out, leaving a^2-b^2 I don't believe that FOIL applies exclusively to terms with exponents, but just with multiplying any two binomials (If I recall correctly, that would imply something like (a+b)(c+d). If you have a term in parentheses and squared, then that's the same as writing it once and times itself, then FOIL would apply. But you can still use foil with (6+2)(3-7) or something. (6+2)(3-7) +12 -42 +6 -14 = -38 ...Yeah. Yeah, that's basic use of the distributive property. If you have a number or expression in front of an expression in brackets, you can multiply the two numbers or expressions together. Now, try this one... lna - lnb = ln(a/b)
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Posted: Sat May 16, 2009 5:10 pm
Marisarin Histale Yeah, that's basic use of the distributive property. If you have a number or expression in front of an expression in brackets, you can multiply the two numbers or expressions together. Now, try this one... lna - lnb = ln(a/b) Arrrrgh! My brain is melting!
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Posted: Sat May 16, 2009 10:06 pm
This is an extremely silly question. To see why, just rearrange the right side.
a^2 - b^2 = a^2 - b^2 + ab - ab
All the right side is, is the left side with (-ab + ab) added to it, which is nothing more than (+ 0).
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Posted: Sun May 17, 2009 6:08 am
I don't even understand the question. Are we being asked to find the factors?
i.e. a^2 - b^2 = (a-b)(a+b)?
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Posted: Sun May 17, 2009 6:49 am
Morberticus I don't even understand the question. Are we being asked to find the factors? i.e. a^2 - b^2 = (a-b)(a+b)? I see no point in finding the factors since neither side is factored. The right side is just the left side with zero added to it, so whatever is being asked is just silly.
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Posted: Sun May 17, 2009 8:33 am
zz1000zz Morberticus I don't even understand the question. Are we being asked to find the factors? i.e. a^2 - b^2 = (a-b)(a+b)? I see no point in finding the factors since neither side is factored. The right side is just the left side with zero added to it, so whatever is being asked is just silly. Ahh... I didn't see the poll until now.
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