Question

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

Answer 1

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`