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

Question

appleduardo · Answer

$$(2^{2} + 3x ) ^{4}$$

calculusfunctions · Answer

In other words, your question is simplify$$(4+3x)^{4}$$Correct?

calculusfunctions · Answer

Do you know the binomial theorem?

calculusfunctions · Answer

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

appleduardo · Answer

yeep i do, (pascal's triangle)

calculusfunctions · Answer

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

calculusfunctions · Answer

1
                                                     1    1
                                                  1    2    1
                                               1    3    3    1
                                             1   4     6    4   1
                                                          .
                                                          .
                                                          .

appleduardo · Answer

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

calculusfunctions · Answer

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

calculusfunctions · Answer

What is your final answer after you simplify?

calculusfunctions · Answer

Do you know how to simplify it further?

calculusfunctions · Answer

Yes or no?

appleduardo · Answer

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

appleduardo · Answer

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

appleduardo · Answer

is that correct?

calculusfunctions · Answer

Very Good!

appleduardo · Answer

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

calculusfunctions · Answer

Welcome anytime!