Question

Multiply:
$\left(\frac{1}{3}{x}^2-\frac{1}{2}x+5\right)by\left(\frac{1}{2}{x}^2-\frac{1}{3}x+1\right)$

Answer 1

$(\frac{1}{3}{x}^2-\frac{1}{2}x+5)\ast (\frac{1}{2}{x}^2-\frac{1}{3}x+1)$

$=\frac{1}{6}{x}^4-\frac{1}{9}{x}^3+\frac{1}{3}{x}^2-\frac{1}{4}{x}^3+\frac{1}{6}{x}^2-\frac{1}{2}x+\frac{5}{2}{x}^2-\frac{5}{3}x+5$

$=\frac{1}{6}{x}^4-\frac{13}{36}{x}^3+\frac{2+1+15}{6}{x}^2-\frac{13}{6}x+5$

$=\frac{1}{6}{x}^4-\frac{13}{36}{x}^3+3x^2-\frac{13}{6}x+5$