How do you use the binomial (2t-s)^5(2ts)5 using Pascal's triangle?

1 Answer
Jul 10, 2017

(2t-s)^5=32 t^5-80st^4 +80s^2t^3- 40t^2s^3+ 10ts^4 -s^5(2ts)5=32t580st4+80s2t340t2s3+10ts4s5

Explanation:

Pascal's triangle:

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The sixth row, which corresponds to a binomial raised to the fifth power, shows us the coefficient of each term of that expansion. So the first term has coefficient 11, the second term 66, etc.

We also know that, for a binomial raised to nn, one nomial in each term will have decreasing exponents from nn to 00 and the other nomial will have increasing exponents from 00 to nn.

therefore(2t-s)^5=1(2t)^5(-s)^0+6(2t)^4(-s)^1+10(2t)^3(-s)^2+10(2t)^2(-s)^3+6(2t)^1(-s)^4+1(2t)^0(-s)^5
=32 t^5-80st^4 +80s^2t^3- 40t^2s^3+ 10ts^4 -s^5