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

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Answer 1 · 2017-01-21T21:23:35

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

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:
$x^5+15x^4+90x^3+270*x^2+405*x+243$

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