How do you multiply #( x - 3) ( 2x ^ { 2} - 3x - 4)#?

1 Answer
smendyka
Jul 16, 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)(x) - color(red)(3))(color(blue)(2x^2) - color(blue)(3x) - color(blue)(4))# becomes:

#(color(red)(x) xx color(blue)(2x^2)) - (color(red)(x) xx color(blue)(3x)) - (color(red)(x) xx color(blue)(4)) - (color(red)(3) xx color(blue)(2x^2)) + (color(red)(3) xx color(blue)(3x)) + (color(red)(3) xx color(blue)(4))#

#2x^3 - 3x^2 - 4x - 6x^2 + 9x + 12#

We can now group and combine like terms:

#2x^3 - 3x^2 - 6x^2 - 4x + 9x + 12#

#2x^3 + (-3 - 6)x^2 + (-4 + 9)x + 12#

#2x^3 + (-9)x^2 + 5x + 12#

#2x^3 - 9x^2 + 5x + 12#

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