Answer
$24\pi x^2+72\pi x+54\pi$
Work Step by Step
Where r is the radius of the cylinder and h is its height, the surface area of a cylinder is
$2\pi r^2+2\pi rh$
Substitute the given values for r and h, and simplify the expression.
$2\pi(2x+3)^2+2\pi(2x+3)[2(2x+3)]\longrightarrow$ rewrite the square;use the distributive property to multiply by 2
$2\pi(2x+3)(2x+3)+2\pi(2x+3)(4x+6)\longrightarrow$ use FOIL to multiply the binomials
$2\pi(4x^2+6x+6x+9)+2\pi(8x^2+12x+12x+18)\longrightarrow$ combine like terms
$2\pi(4x^2+12x+9)+2\pi(8x^2+24x+18)\longrightarrow$ factor out $2\pi$
$2\pi(4x^2+12x+9+8x^2+24x+18)\longrightarrow$ combine like terms
$2\pi(12x^2+36x+27)\longrightarrow$ use the distributive property to write in standard form
$24\pi x^2+72\pi x+54\pi$
