anonymous
  • anonymous
Use the Binomial Theorem to expand the binomial and express the result in simplified form. (5x-5y)3
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
Help much appreciated!
Nnesha
  • Nnesha
\[\huge\rm (a+b)^3=1a^3+3a^2b+3ab^2+b^3\]
Nnesha
  • Nnesha
you can use pascal's triangle for the coefficient and the exponent of first term start from highest degree to 0 and the exponent of 2nd term start from 0 to highest degree |dw:1443580070541:dw| like in this example power of first term is decreasing and 2nd term exponents are increasing

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Nnesha
  • Nnesha
make sense or no ???
anonymous
  • anonymous
\[15z-15y?\]
Nnesha
  • Nnesha
the numbers in red color r from the pascal's triangle|dw:1443580345523:dw| 3rd row
anonymous
  • anonymous
So in this case, you would use the third row of pascal's triangle? Since it's to the third power?
Nnesha
  • Nnesha
yes right
Nnesha
  • Nnesha
but remember it starts from 0 |dw:1443580628444:dw|
Nnesha
  • Nnesha
an y question ? can u solve ur question nw ??
anonymous
  • anonymous
I'm still kind of confused... do you multiply the coefficients of the binomial's terms (that are being raised to a certain power), by the numbers of the specified Pascal's Triangle row?
Nnesha
  • Nnesha
yes in ur question there are numbers in first and term so you should multiply the coefficient by the coefficient of the term |dw:1443581219197:dw| now u should multiply the coefficient one by 5^3
Nnesha
  • Nnesha
\[\large \rm (5x-5y)^3=\color{ReD}{1}(5x)^\color{blue}{3}(-5y)^0+\color{reD}{3}(5x)^\color{blue}{2}(-5y)^1.......+\] as u can see power of first term is decreasing andexponent of 2nd terms is increasing
Nnesha
  • Nnesha
-3(5x)^2(-5y)^1 = ????

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