How do you use the binomial (2t-s)^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

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 1, the second term 6, etc.

We also know that, for a binomial raised to n, one nomial in each term will have decreasing exponents from n to 0 and the other nomial will have increasing exponents from 0 to n.

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