anonymous
  • anonymous
Expand (2x + y)5.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Have you drawn yourself a triangle. It looks like you may need one.
anonymous
  • anonymous
This Is A Binomial Theorem
anonymous
  • anonymous
OH yes. You can use combinations to figure out the coefficients or just keep drawing the triangle. The triangle is quicker until you get to some higher powers.

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anonymous
  • anonymous
Is There A Formula For This ?
UnkleRhaukus
  • UnkleRhaukus
\[(a+b)^n=\sum_{k=0}^n\begin{pmatrix}n\\k\end{pmatrix}a^{n-k}b^k\] \[\begin{align} (a+b)^1&=1(a+b)&&=a+b\\ (a+b)^2&=1a^2b^0+2a^1b^1+1a^0b^2&&=a^2+2ab+b^2\\ (a+b)^3&=1a^3b^0+3a^2b^1+3a^1b^2+a^0b^3&&=a^3+3a^2b+3ab^2+b^3\\ \vdots \end{align}\]
anonymous
  • anonymous
Are you good with the formula above?
anonymous
  • anonymous
I Think So.... I Just Plug Everything Inside ?
anonymous
  • anonymous
Yes. As long as you have the rows of the triangle on paper it's not a big deal. Just notice the pattern of how the exponents change and be careful when negatives are being raised to powers.
anonymous
  • anonymous
No Im Lost !
anonymous
  • anonymous
Let walk through it. There is a lot to do for a full expansion. Triangle row ----> 1 5 10 10 5 1 (Good?)
UnkleRhaukus
  • UnkleRhaukus
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anonymous
  • anonymous
What Is the Triangle Row And What Am I Suppose To Do With It ?
anonymous
  • anonymous
UncleRhaukus drew the Pascal's Triangle above. Each row represents the coefficients of the terms if we were just doing (a + b) to a power. The first row is power=0. Notice the second number on the row is actually our power. The expansion looks like this. I am only giving the answer in part for your analysis. 1 * (2x)^5 * (y)^0 this is the first term, notice exponents add up to 5. 5 * (2x)^4 * (y)^1 this is the second term 10 * (2x)^3 * (y)^2 this is the third term ^ ^ ^ ^ ^ ^ 2nd term of binomial ^ 1st term of binomial numbers from the triangle
UnkleRhaukus
  • UnkleRhaukus
|dw:1370155564079:dw|
anonymous
  • anonymous
Combination format. Do you understand this mbanks12?
anonymous
  • anonymous
Try using binomial expansion. The general form of a term in a binomial expansion is: nCr(First Term) ^ r (Second Term)^ (n-r) where r is the rth term of the progression (work from 0 to 5) and n is 5. The operation aCb means a!/(a! * (b-a)!)
anonymous
  • anonymous
*Sorry, aCb is a!/(a! * (a-b)!)

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