How do you expand #(x + 3)^5#?

1 Answer
MrsRudolph221
Jan 21, 2017

Row 5 of Pascal's Triangle goes: #1, 5, 10, 10, 5, 1#.

Explanation:

Now use those as the coefficients of each term of your expansion:
#1(x^5)(3^0)+5(x^4)(3^1)+10(x^3)(3^2)+10(x^2)(3^3)+5(x^1)(3^4)+1(x^0)(3^5)#

Notice that the powers of x decrease as the powers of 3 increase. Each time, their sum of powers is still 5.

Simplify each term:
#x^5+5*3x^4+10*9x^3+10*27*x^2+5*81*x+243#

and finally:
#x^5+15x^4+90x^3+270*x^2+405*x+243#

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