To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
(color(red)(2x) - color(red)(3))(color(blue)(x^2) + color(blue)(5x) - color(blue)(3))(2x−3)(x2+5x−3) becomes:
(color(red)(2x) xx color(blue)(x^2)) + (color(red)(2x) xx color(blue)(5x)) - (color(red)(2x) xx color(blue)(3)) - (color(red)(3) xx color(blue)(x^2)) - (color(red)(3) xx color(blue)(5x)) + (color(red)(3) xx color(blue)(3))(2x×x2)+(2x×5x)−(2x×3)−(3×x2)−(3×5x)+(3×3)
2x^3 + 10x^2 - 6x - 3x^2 - 15x + 92x3+10x2−6x−3x2−15x+9
We can now group and combine like terms:
2x^3 + 10x^2 - 3x^2 - 6x - 15x + 92x3+10x2−3x2−6x−15x+9
2x^3 + (10 - 3)x^2 + (-6 - 15)x + 92x3+(10−3)x2+(−6−15)x+9
2x^3 + 7x^2 + (-21)x + 92x3+7x2+(−21)x+9
2x^3 + 7x^2 - 21x + 92x3+7x2−21x+9
