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

1 Answer
Don't Memorise
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)#

#=2x^4+5x^3+9x^2 +6x^3+15x^2+27x - 4x^2 -10x -18#

Grouping like terms:
#=2x^4+(5x^3 +6x^3)+(9x^2 - 4x^2+15x^2)+(27x -10x) -18#

#=2x^4+11x^3+20x^2 +17x -18#

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