Expand \(( 3+x)^5 \)

\begin{align} & (1) (3)^5(x)^0 = 243 \\ + & (5) (3)^4(x)^1= 405x \\ + & (10)(3)^3(x)^2= 270x^2 \\ + & (10)(3)^2(x)^3=90x^3 \\ + & (5)(3)^1(x)^4= 15x^4\\ + & (1)(3)^0(x)^5= x^5 \\ \\ \therefore \quad (3+x)^5 & =243+405x+270x^2+90x^3+15x^4+x^5 \end{align}

Expand \(( 3-2x)^5 \)

\begin{align} & (1) (3)^5(-2x)^0 = 243 \\ + & (5) (3)^4(-2x)^1= -810x \\ + & (10)(3)^3(-2x)^2= 1080x^2 \\ + & (10)(3)^2(-2x)^3= -720x^3 \\ + & (5)(3)^1(-2x)^4= 240x^4\\ + & (1)(3)^0(-2x)^5= -32x^5 \\ \\ \therefore \quad (3-2x)^5 & =243-810x+1080x^2-720x^3+240x^4-32x^5 \end{align}