53.8k views
1 vote
Binomial ( 5x - y ) ^ 10 terms ax ^ 2 y ^8

1 Answer

2 votes

\bf (5x-y)^(10)\implies \begin{array}{llll} term&coefficient&value\\ -----&-----&-----\\ 1&+1&(5x)^(10)(-y)^0\\ 2&+10&(5x)^9(-y)^1\\ 3&+45&(5x)^8(-y)^2\\ 4&+120&(5x)^7(-y)^3\\ 5&+210&(5x)^6(-y)^4\\ 6&+252&(5x)^5(-y)^5\\ 7&+210&(5x)^4(-y)^6\\ 8&+120&(5x)^3(-y)^7\\ 9&+45&(5x)^2(-y)^8 \end{array}

now, how do we get the coefficients? well, the first coefficient is 1, any subsequent is " the product of the current terms's coefficient and the exponent of the first element, divided by the exponent of the second element in the next term", now that's a mouthful, but for example,

how did get 210 for the 5th expanded term? well is just 120 * 7 / 4

how about 252 of the 6th term? 210 * 6 / 5.

how about 45 of the 9th one? 120 * 3 / 8.

of course, the exponents for each is simple, as you'd already know from the binomial theorem.

so, just expand away the 9th expanded term.
User Adam DiCarlo
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories