How do you simplify #(x - 1)(x^3 + 2x^2 + 2)#?

1 Answer
smendyka
Jul 1, 2018

See a solution process below:

Explanation:

To simplify 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)(1))(color(blue)(x^3) + color(blue)(2x^2) + color(blue)(2))# becomes:

#(color(red)(x) xx color(blue)(x^3)) + (color(red)(x) xx color(blue)(2x^2)) + (color(red)(x) xx color(blue)(2)) - (color(red)(1) xx color(blue)(x^3)) - (color(red)(1) xx color(blue)(2x^2)) - (color(red)(1) xx color(blue)(2))#

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

We can now group and combine like terms:

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

#x^4 + 2x^3 - 1x^3 - 2x^2 + 2x - 2#

#x^4 + (2 - 1)x^3 - 2x^2 + 2x - 2#

#x^4 + 1x^3 - 2x^2 + 2x - 2#

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

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