To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
(color(red)(3d) + color(red)(3))(color(blue)(2d^2) + color(blue)(5d) - color(blue)(2))(3d+3)(2d2+5d−2) becomes:
(color(red)(3d) xx color(blue)(2d^2)) + (color(red)(3d) xx color(blue)(5d)) - (color(red)(3d) xx color(blue)(2)) + (color(red)(3) xx color(blue)(2d^2)) + (color(red)(3) xx color(blue)(5d)) - (color(red)(3) xx color(blue)(2))(3d×2d2)+(3d×5d)−(3d×2)+(3×2d2)+(3×5d)−(3×2)
6d^3 + 15d^2 - 6d + 6d^2 + 15d - 66d3+15d2−6d+6d2+15d−6
We can now group and combine like terms:
6d^3 + 15d^2 + 6d^2 - 6d + 15d - 66d3+15d2+6d2−6d+15d−6
6d^3 + (15 + 6)d^2 + (-6 + 15)d - 66d3+(15+6)d2+(−6+15)d−6
6d^3 + 21d^2 + 9d - 66d3+21d2+9d−6
