cookiimonster627
  • cookiimonster627
Expand the binomials using the Binomial theorem. (2x+3y)^4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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campbell_st
  • campbell_st
binomial theorem says \[(a + b)^n = \left(\begin{matrix}n \\ r\end{matrix}\right) \sum_{n = 0}^{k}(a)^{n - k}(b)^k\]
cookiimonster627
  • cookiimonster627
how do I figure it out
campbell_st
  • campbell_st
ok... so a = 2x and b = 3y and n = 4 so rather than using combinations to get the initial coefficient you can just use Pascal's Triangle so its 1, 4, 6, 4, 1 so the then terms are \[1 \times (2x)^4(3y)^0 + 4 \times (2x)^4(3y)^1 + 6 \times (2x)^3 (3y)^2+...\] so as the power of (2x) decreases the power of (3y) increases... there are 5 terms... so when you have all 5 just multiply the coefficients \[16x^4 + 4 \times 8x^3\times2y+ ..... \]

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campbell_st
  • campbell_st
hope it makes sense
cookiimonster627
  • cookiimonster627
yea thank you
campbell_st
  • campbell_st
opps I think I got the powers and sum from and to.. round the wrong way
cookiimonster627
  • cookiimonster627
what do you mean?

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