Which of the following is the expansion of (x + 3)^5?

Question

anonymous · Answer

alright, so first start of by making pascal's triangle.

             1         (constant)
          1    1       (a+b)^1
       1    2    1    (a+b)^2
     1   3    3    1 (a+b)^3
  1   4    6    4    1   (a+b)^4
1   5  10  10   5   1  (a+b)^5

rayford · Answer

here are the answer choices: x5 + 5x4 + 10x3 + 10x2 + 5x + 1

 x5 + 3x4 + 9x3 + 27x2 + 81x + 243

 x5 + 15x4 + 90x3 + 270x2 + 405x + 243

 None of the above

anonymous · Answer

what these mean is that is if you have

$$(a+b)^n$$

the expansion will be

$$c_1 a^n+c_2 a^{n-1}b^{n-4}+c_3 a^{n-2}b^{n-3}+c_4 a^{n-3}b^{n-2}+c_5 a^{n-4}....... $$where the c's are the numbers on the triangle

anonymous · Answer

so fro (x+5)^5.. you have x=a, and b=5

lookingat the triangle for the 5th power

rayford · Answer

so it's none of the above obviously?

rayford · Answer

am i correct?

anonymous · Answer

so your first is going to x^5

anonymous · Answer

second term is $$5x^4*3=5x^4(b)=15x^4$$

anonymous · Answer

next term is
$$10x^{n-2}b{n-3}=10x^3*3^2=90x^3$$