anonymous
  • anonymous
I need help with binomial expansions using Pascal's Triangle. The binomial I am using is (b - 2)^4. First, I know you set up the problem like this: 1 4 6 4 1 But I don't know where to go from there. Could anyone help me?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Alright so you know you have the co-efficients \[\{1\phantom{s}4\phantom{s}6\phantom{s}4\phantom{s}1\}\] So you set up your equation like this: \[(b-2)^4=(1)(b)^4(-2)^0+(4)(b)^3(-2)^1+(6)(b)^2(-2)^2+4(b)^1(-2)^3+1(b)^0(-2)^4\]
anonymous
  • anonymous
And you and you can simplify so you would have: \[\eqalign{ (b-2)^4&=(1)(b)^4(-2)^0+(4)(b)^3(-2)^1+(6)(b)^2(-2)^2+4(b)^1(-2)^3+1(b)^0(-2)^4 \\ &=b^4-8b^3+24b^2-32b+16 }\]
anonymous
  • anonymous
Thank you, that helped so much! I'm still kinda confused on the exponents part though, do you just put them in reverse order?

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anonymous
  • anonymous
Yeah! Well the thing is if you notice, the exponents of the variable (in this case, \(b\) ) start at the original exponent \((4)\) and decrease to zero. And the exponents of the constant (in this case, the \((-2)\) ) start at zero and work their way up to the original exponent \((4)\). And each term uses their respective Pascalian Binomial Co-efficient one by one!
anonymous
  • anonymous
Thank you so much, I understand it now! :)
anonymous
  • anonymous
Great! Im real happy :)

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