I dont know if that's the correct terminology, but I can't find a basic tutorial on solving something like this:
http://i43.tinypic.com/13zux38.jpg
How would you expand that, and can you explain how you knew/what model you used?
Thanks
I dont know if that's the correct terminology, but I can't find a basic tutorial on solving something like this:
http://i43.tinypic.com/13zux38.jpg
How would you expand that, and can you explain how you knew/what model you used?
Thanks
Ah okay, $\displaystyle -5(x+\Delta x)^{3}$. Ignore the -5 at the front for now. Expanding $\displaystyle (x+\Delta x)^{3}$, you would get $\displaystyle x^{3}+3x^{2}\Delta x+3x(\Delta x)^{2}+(\Delta x)^{3}$.
Notice the descending powers on the first term $\displaystyle x$ and the ascending powers of the second term $\displaystyle \Delta x$. The coefficients of each term (i.e. 1, 3, 3, 1) come from the 4th line of Pascal's triangle, if you know what that is.
Or, the coefficient of the first term in an expansion like this is always $\displaystyle \left( \begin{array}{c} n \\ C \\ 0 \end{array} \right)$
$\displaystyle n$ is the power of the bracket, so in your case, $\displaystyle n=3$. The second coefficient is $\displaystyle \left( \begin{array}{c} n \\ C \\ 1 \end{array} \right)$. This goes on up until $\displaystyle \left( \begin{array}{c} n \\ C \\ n \end{array} \right)$.
The first one comes from $\displaystyle \left( \begin{array}{c} 3 \\ C \\ 0 \end{array} \right)$
Second one from $\displaystyle \left( \begin{array}{c} 3 \\ C \\ 1 \end{array} \right)$
Third one from $\displaystyle \left( \begin{array}{c} 3 \\ C \\ 2 \end{array} \right)$
And fourth one from $\displaystyle \left( \begin{array}{c} 3 \\ C \\ 3 \end{array} \right)$
Then finally, you just multiply each of the terms by that $\displaystyle -5$ we left out to finally get $\displaystyle -5x^{3}-15x^{2}(\Delta x)-15x(\Delta x)^{2}-5(\Delta x)^{3}$
Hope that helps and it's not too much of a wordy explanation. Feel free to reply with any more Qs