How do you simplify #(x - 9)(x - 2)(3x + 2)#?

1 Answer
Jun 7, 2017

Answer:

See a solution process below:

Explanation:

First, multiply the two terms on the right. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(x - 9)(color(red)(x) - color(red)(2))(color(blue)(3x) + color(blue)(2))# becomes:

#(x - 9)((color(red)(x) xx color(blue)(3x)) + (color(red)(x) xx color(blue)(2)) - (color(red)(2) xx color(blue)(3x)) - (color(red)(2) xx color(blue)(2)))#

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

We can now combine like terms:

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

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

#(x - 9)(3x^2 - 4x - 4)#

Now, do the same thing for the two remaining terms:

#(color(red)(x) - color(red)(9))(color(blue)(3x^2) - color(blue)(4x) - color(blue)(4))# becomes:

#(color(red)(x) xx color(blue)(3x^2)) - (color(red)(x) xx color(blue)(4x)) - (color(red)(x) xx color(blue)(4)) - (color(red)(9) xx color(blue)(3x^2)) + (color(red)(9) xx color(blue)(4x)) + (color(red)(9) xx color(blue)(4))#

#3x^3 - 4x^2 - 4x - 27x^2 + 36x + 36#

We can now group and combine like terms:

#3x^3 - 4x^2 - 27x^2 - 4x + 36x + 36#

#3x^3 + (-4 - 27)x^2 + (-4 + 36)x + 36#

#3x^3 + (-31)x^2 + 32x + 36#

#3x^3 - 31x^2 + 32x + 36#