How do you evaluate #(a + 8) ( 2a ^ { 2} - a + 8)#?

1 Answer
smendyka
Mar 23, 2017

See the entire 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)(a) + color(red)(8))(color(blue)(2a^2) - color(blue)(a) + color(blue)(8))# becomes:

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

#2a^3 - a^2 + 8a + 16a^2 - 8a + 64#

We can now group and combine like terms:

#2a^3 - a^2 + 16a^2 + 8a - 8a + 64#

#2a^3 - 1a^2 + 16a^2 + 8a - 8a + 64#

#2a^3 + (-1 + 16)a^2 + (8 - 8)a + 64#

#2a^3 + 15a^2 + 0a + 64#

#2a^3 + 15a^2 + 64#

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