## Algebra 1: Common Core (15th Edition)

$V=\displaystyle \frac{4}{3}\pi x^{3}+12\pi x^{2}+36\pi x+36\pi$
$V=\displaystyle \frac{4}{3}\pi r^{3}$...the volume of a sphere with a radius r. $r=x+3$...substitute $x+3$ with $r$in the formula. $V=\displaystyle \frac{4}{3}\pi(x+3)^{3}$...write $(x+3)^{3}$ as $(x+3)^{2}\cdot(x+3)^{1}$. $V=\displaystyle \frac{4}{3}\pi(x+3)^{2}\cdot(x+3)$...square the binomial. $V=\displaystyle \frac{4}{3}\pi(x^{2}+2(x)(3)+3^{2})\cdot(x+3)$ ...simplify the first parentheses. $V=\displaystyle \frac{4}{3}\pi(x^{2}+6x+9)\cdot(x+3)$ ...distribute. $V=\displaystyle \frac{4}{3}\pi[(x^{2}+6x+9)\cdot x+(x^{2}+6x+9)\cdot 3]$ ...distribute. $V=\displaystyle \frac{4}{3}\pi(x^{3}+6x^{2}+9x+3x^{2}+18x+27)$ ...simplify. $V=\displaystyle \frac{4}{3}\pi(x^{3}+9x^{2}+27x+27)$ ...distribute. $V=\displaystyle \frac{4}{3}\pi x^{3}+12\pi x^{2}+36\pi x+36\pi$