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

1 Answer
smendyka
May 21, 2017

See a solution process below:

Explanation:

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))# 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^3 + 10x^2 - 6x - 3x^2 - 15x + 9#

We can now group and combine like terms:

#2x^3 + 10x^2 - 3x^2 - 6x - 15x + 9#

#2x^3 + (10 - 3)x^2 + (-6 - 15)x + 9#

#2x^3 + 7x^2 + (-21)x + 9#

#2x^3 + 7x^2 - 21x + 9#

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