How do you multiply (x^2 + 3x - 2)(2x^2 + 5x + 9)?

Jul 31, 2015

=color(blue)(2x^4+11x^3+20x^2 +17x -18

Explanation:

color(blue)((x^2+3x−2))(2x^2+5x+9)

We need to multiply each term within the first bracket with all three terms of the second bracket.

=color(blue)((x^2))(2x^2+5x+9) +color(blue)(3x)(2x^2+5x+9) −color(blue)((2))(2x^2+5x+9)

$= 2 {x}^{4} + 5 {x}^{3} + 9 {x}^{2} + 6 {x}^{3} + 15 {x}^{2} + 27 x - 4 {x}^{2} - 10 x - 18$

Grouping like terms:
$= 2 {x}^{4} + \left(5 {x}^{3} + 6 {x}^{3}\right) + \left(9 {x}^{2} - 4 {x}^{2} + 15 {x}^{2}\right) + \left(27 x - 10 x\right) - 18$

$= 2 {x}^{4} + 11 {x}^{3} + 20 {x}^{2} + 17 x - 18$