3u^4 - 24uv³
The above expression needs to be factored. The expression can be factored by following the [b]difference of cubes[/b] formula.
a³ - b³ = (a-b)(a²+ab+b²)
But no matter how hard I try to understand what's going on, the example still seems like numbers are being pulled out of a hat.
3u^4 - 24uv³ = 3u(u³ - 8v³)
3u(u³ - 8v³) = 3u(u³ - (2v)³)
3u(u³ - (2v)³) = 3u(u-2v)(u²+2uv+4v²)
What am I looking at? I guess I understand the "3u^4 - 24uv³ = 3u(u³ - 8v³)" bit but beyond that I go brain-dead.
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3u(u^3 - 8v^3) I simply took out the integer 3 and the variable U. But if you are having trouble figuring that out for different problems, let me attempt to describe it for you: It's like a game in which you hunt down any similarities between 2 or three sets of numbers in an expression and then drag those similarities out of the group and [b]set it up as a multiplication problem that would result in the original expression you were given.[/b] 75x+100x = 25x(3+4) or more complex: 28x^2y^4-70x^3y+14x^2Y^4 = 14x^2y(2y^3 - 5x + y^3)
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Edited by A Forum Cop: 1/5/2014 8:35:47 PMI'm gonna starts at the point where you're stuck: 3u^4 - 24uv³ = 3u(u³ - 8v³) The next step simplifies the 8v³ inside the parenthesis(by making it one value cubed, to make it usable in the formula). The cube root of 8 is 2, and the cube root of v³ is, so the cube root of 8v³ is (2v)³. That makes 3u(u³ - 8v³) = 3u(u³ - (2v)³) After that you use the difference of cubes formula and plug in the values for a and b.
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5 RepliesEdited by DarkSpyda04: 1/5/2014 8:20:47 PMNow just roll with me here but if a = u and b = 2v then we could follow the formula like so: (a-b)(a²+ab+b²) (u-2v)(u²+2uv+2v²) But instead we get this: 3u(u-2v)(u²+2uv+4v²) Why? How does b² which should be 2v² amount to 4v²? This is where I start to go stupid. But I guess if b now means something else entirely, 2+2 = fish
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I have the answer, but you're not going to like it.... The meaning of life, the universe, and everything is... 42!
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I have no idea but I'll bump your thread anyway. Try a math forum?
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Uh 24. [spoiler]i'm not good with math[/spoiler]
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1 Reply2^3=8 for the second one...think about it the third one is pretty straightforward, all you do is distribute and then cancel out