How do you multiply #(- 7a ^ { 2} + 3a - 7) ( - 8a ^ { 2} - 6a + 8)#?

1 Answer
smendyka
Jul 24, 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)(-7a^2) + color(red)(3a) - color(red)(7))(color(blue)(-8a^2) - color(blue)(6a) + color(blue)(8))# becomes:

#(color(red)(7a^2) xx color(blue)(8a^2)) + (color(red)(7a^2) xx color(blue)(6a)) - (color(red)(7a^2) xx color(blue)(8)) - (color(red)(3a) xx color(blue)(8a^2)) - (color(red)(3a) xx color(blue)(6a)) + (color(red)(3a) xx color(blue)(8)) + (color(red)(7) xx color(blue)(8a^2)) + (color(red)(7) xx color(blue)(6a)) - (color(red)(7) xx color(blue)(8))#

#56a^4 + 42a^3 - 56a^2 - 24a^3 - 18a^2 + 24a + 56a^2 + 42a - 56#

We can now group and combine like terms:

#56a^4 + 42a^3 - 24a^3 - 56a^2 - 18a^2 + 56a^2 + 24a + 42a - 56#

#56a^4 + (42 - 24)a^3 + (-56 - 18 + 56)a^2 + (24 + 42)a - 56#

#56a^4 + 18a^3 + (-18)a^2 + 66a - 56#

#56a^4 + 18a^3 - 18a^2 + 66a - 56#

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