How do you multiply #(s - 1) ( - 2s ^ { 2} + s - 1)#?

1 Answer
smendyka
Jan 15, 2018

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)(s) - color(red)(1))(color(blue)(-2s^2) + color(blue)(s) - color(blue)(1))# becomes:

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

#-2s^3 + s^2 - s + 2s^2 - s + 1#

We can now group and combine like terms:

#-2s^3 + s^2 + 2s^2 - s - s + 1#

#-2s^3 + 1s^2 + 2s^2 - 1s - 1s + 1#

#-2s^3 + (1 + 2)s^2 + (-1 - 1)s + 1#

#-2s^3 + 3s^2 + (-2)s + 1#

#-2s^3 + 3s^2 - 2s + 1#

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