What is the product of #(x ^ { 2} + 5x) ( x ^ { 3} + 4x ^ { 2} )#?

1 Answer
smendyka
Feb 4, 2017

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(x^2) + color(red)(5x))(color(blue)(x^3) + color(blue)(4x^2))# becomes:

#(color(red)(x^2) xx color(blue)(x^3)) + (color(red)(x^2) xx color(blue)(4x^2)) + (color(red)(5x) xx color(blue)(x^3)) + (color(red)(5x) xx color(blue)(4x^2))#

#x^5 + 4x^4 + 5x^4 + 20x^3#

We can now combine like terms:

#x^5 + (4 + 5)x^4 + 20x^3#

#x^5 + 9x^4 + 20x^3#

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