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

1. appleduardo

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

2. calculusfunctions

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

3. calculusfunctions

Do you know the binomial theorem?

4. calculusfunctions

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

5. appleduardo

yeep i do, (pascal's triangle)

6. calculusfunctions

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

7. calculusfunctions

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

8. appleduardo

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

9. calculusfunctions

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

10. calculusfunctions

11. calculusfunctions

Do you know how to simplify it further?

12. calculusfunctions

Yes or no?

13. appleduardo

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

14. appleduardo

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

15. appleduardo

is that correct?

16. calculusfunctions

Very Good!

17. appleduardo

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

18. calculusfunctions

Welcome anytime!