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: 29

Answer

$4\pi x^2+22\pi x+28\pi$

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. $2\pi(x+2)^2+2\pi(x+2)(x+5)\longrightarrow$ rewrite the square $2\pi(x+2)(x+2)+2\pi(x+2)(x+5)\longrightarrow$ use FOIL to multiply the binomials $2\pi(x^2+2x+2x+4)+2\pi(x^2+5x+2x+10)\longrightarrow$ combine like terms $2\pi(x^2+4x+4)+2\pi(x^2+7x+10)\longrightarrow$ factor out $2\pi$ $2\pi(x^2+4x+4+x^2+7x+10)\longrightarrow$ combine like terms $2\pi(2x^2+11x+14)\longrightarrow$ use the distributive property to write in standard form $4\pi x^2+22\pi x+28\pi$
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