How do you multiply #(- 2x - \frac { 2} { 3} ) ( 6x + \frac { 9} { 4} )#?

1 Answer
smendyka
Jul 4, 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)(2/3))(color(blue)(6x) + color(blue)(9/4))# becomes:

#-(color(red)(2x) xx color(blue)(6x)) - (color(red)(2x) xx color(blue)(9/4)) - (color(red)(2/3) xx color(blue)(6x)) - (color(red)(2/3) xx color(blue)(9/4))#

#-12x - (color(red)(color(black)(cancel(color(red)(2)))x) xx color(blue)(9/(color(black)(cancel(color(blue)(4)))2))) - (color(red)(2/color(black)(cancel(color(red)(3)))) xx color(blue)(color(black)(cancel(color(blue)(6)))2x)) - (color(red)(color(black)(cancel(color(red)(2)))/color(black)(cancel(color(red)(3)))) xx color(blue)(color(black)(cancel(color(blue)(9)))3)/(color(black)(cancel(color(black)(4)))2)))#

#-12x^2 - 9/2x - 4x - 3/2#

We can now combine like terms:

#-12x^2 - 9/2x - (2/2 xx 4)x - 3/2#

#-12x^2 - 9/2x - 8/2x - 3/2#

#-12x^2 + (-9/2 - 8/2)x - 3/2#

#-12x^2 + (-17/2x) - 3/2#

#-12x^2 - 17/2x - 3/2#

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