Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 8 - Polynomials and Factoring - 8-3 Multiplying Binomials - Practice and Problem-Solving Exercises - Page 490: 30


$24\pi x^2+72\pi x+54\pi$

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 $24\pi x^2+72\pi x+54\pi$
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