Simplify (√2 + √3)² - (√2 - √3)²
- Thread starter znick46
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We'll be glad to explain! Please reply with a clear listing of your steps, so we can figure out where things went sideways, and reply with explanations.
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Or, how about x^2-y^2 = (x-y)(x+y) where x = Sqrt(2) + Sqrt(3) and y = Sqrt(2) - Sqrt(3)
Add x to y, subtract y from x, multiply the two results. You can pretty much jot down the computations if you see method. A good double check if nothing else.
Or, how about x^2-y^2 = (x-y)(x+y) where x = Sqrt(2) + Sqrt(3) and y = Sqrt(2) - Sqrt(3)
Add x to y, subtract y from x, multiply the two results. You can pretty much jot down the computations if you see method. A good double check if nothing else.
This is where i'm confused.
- (a - b)^2 turning into - a^2 + 2ab - b^2
isn't this the same as (-a+b)^2 = (-a+b)(-a+b) - then foil to get diffrence of squares a^2 -ab+ab +b^2
Remember PEMDAS. Exponentiation and multiplication happen BEFORE subtraction.
\(\displaystyle -(a - b)^2 = -\{(a - b)(a - b)\} = -\{a * a + a * -(b) - (b) * a + (- b)(- b)\} = -(a^2 - 2ab + b^2) = -a^2 + 2ab - b^2.\)
Notice that FOIL takes place within { and } (as required by PEMDAS) before applying the minus sign.
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znick46, you could also factor this. \(\displaystyle \ \) It's the difference of two squares.
\(\displaystyle (a + b)^2 \ - \ (a - b)^2 \ = \)
\(\displaystyle [(a + b) \ - \ (a - b)][(a + b) \ + \ (a - b)] \ = \)
\(\displaystyle (a \ + \ b \ - \ a \ + \ b)(a \ + \ b \ + \ a \ - \ b) \ = \)
\(\displaystyle (2b)(2a) \ = \)
\(\displaystyle 4ab\)
Can you explain this more in detail, i'm lost after the second step. I'm curious how you did it.