Question

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FORMULAS OF :
✍️TRIGONOMETRY

✍️ BINOMIAL THEOREM
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Answer 1

The binomial theorem can be stated using a summation:

 (x+y)n=∑r=0n((nr)xn−ryr)

This is a very succinct way of summarizing the pattern in a binomial expansion. Let’s return to (x + y)3 to see how the theorem works.

 (x+y)3 =(30)x3−0y0+(31)x3−1y1+(32)x3−2y2+(33)x3−3y3

   =1x3⋅1+3x2y+3xy2+1⋅x0⋅y3

   =x3+3x2y+3xy2+y3

Again, the exponents on x descend from 3 to 0. The exponents on y ascend from 0 to 3. The coefficients on the terms correspond to row 3 of Pascal’s triangle. These coefficients are, not surprisingly, referred to as binomial coefficients!

Given this theorem, we can expand any binomial without having to multiply all of the factors. We can also identify a particular term in an expansion. Before we solve these kinds of problems, we will prove the theorem:

The Binomial Theorem: (x+y)n=∑r=0n((nr)xn−ryr)                                                                                                    

Answer 2

Step-by-step explanation:

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