For Pascal's identity what is the method to finding the exponents? I understand how the coefficients were found but not how the exponents were incremented. Thank you in advance for your help!
You start off with a^n, where n is the highest exponent and b^0 = 1. Then decrease the a exponent by 1 and increase the b exponent by 1 and add each term until you arrive at a^0 and b^n. For example (a+b)^4 = a^4 + 4(a^3)(b) + 6(a^2)(b^2) + 4(a)(b^3) + b^4 If it was (a - b)^4 you would add first, then subtract, then continue alternating between each term.
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![[Discrete Mathematics] Binomial Theorem and Pascal's Triangle](/img/1.gif)
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For Pascal's identity what is the method to finding the exponents? I understand how the coefficients were found but not how the exponents were incremented. Thank you in advance for your help!
Pascals triangle will only help you find the coefficient. You need the binomial theorem to determine the degree of each exponent.
You start off with a^n, where n is the highest exponent and b^0 = 1. Then decrease the a exponent by 1 and increase the b exponent by 1 and add each term until you arrive at a^0 and b^n.
For example (a+b)^4 =
a^4 +
4(a^3)(b) +
6(a^2)(b^2) +
4(a)(b^3) +
b^4
If it was (a - b)^4 you would add first, then subtract, then continue alternating between each term.
Thank you so much! This was so helpful!
Glad I could help!
this really helped a lot! thanks
Thank u
No problem
u here chotu
Hey hope you are doing alright just I wanna say that
GOD loved the world so much he sent his only begotten
son Jesus to die a brutal death for us so that we can have eternal life and we can all accept this amazing gift this by simply trusting in Jesus, confessing that GOD raised him from the dead, turning away from your sins and forming a relationship with GOD.