Mathematics
09.06.2023 06:34
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Binomial ( 5x - y ) ^ 10 terms ax ^ 2 y ^8

Binomial ( 5x - y ) ^ 10 terms ax ^ 2 y ^8
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jakaylathomas11
jakaylathomas11
4,5(6 marks)
\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?ย  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?ย  well is just 120 * 7 / 4

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

how about 45 of the 9th one?ย  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.
nakuhernandez
nakuhernandez
4,7(2 marks)
1/4(n-64) because if you distribute, it becomes:
1/4n - 16

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