appleduardo
whats the result of: (2^(2) + 3x ) ^(4)



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appleduardo
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\[(2^{2} + 3x ) ^{4}\]

calculusfunctions
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In other words, your question is simplify\[(4+3x)^{4}\]Correct?

calculusfunctions
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Do you know the binomial theorem?

calculusfunctions
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Or do you know how to use Pascal's triangle?

appleduardo
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yeep i do, (pascal's triangle)

calculusfunctions
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OK so then you should know what to do, right?

calculusfunctions
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1 1
1 2 1
1 3 3 1
1 4 6 4 1
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appleduardo
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so ill get: (4)^4 + 4(4^(3) * 3x) + 6( 4^(2) * (3x)^(2) + 4 (4) * (3x)^(3) + (3x)^(4) ??

calculusfunctions
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\[(a +b)^{4}=a ^{4}+4a ^{3}b +6a ^{2}b ^{2}+4ab ^{3}+b ^{4}\]Yes your answer is correct. Now simplify!

calculusfunctions
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What is your final answer after you simplify?

calculusfunctions
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Do you know how to simplify it further?

calculusfunctions
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Yes or no?

appleduardo
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im on that!, im finishing and ill post it as soon as i get it done!

appleduardo
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i got: 256 + 768x + 864x^2 + 432x^3 + 81x^4

appleduardo
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is that correct?

calculusfunctions
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Very Good!

appleduardo
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:o thank you so much for being such a great guidence!

calculusfunctions
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Welcome anytime!