How do you simplify the product #(2x^2 + 5x - 3)(2x + 1) # and write it in standard form?

1 Answer
smendyka
May 5, 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)(2x^2) + color(red)(5x) - color(red)(3))(color(blue)(2x) + color(blue)(1))# becomes:

#(color(red)(2x^2) xx color(blue)(2x)) + (color(red)(2x^2) xx color(blue)(1)) + (color(red)(5x) xx color(blue)(2x)) + (color(red)(5x) xx color(blue)(1)) - (color(red)(3) xx color(blue)(2x)) - (color(red)(3) xx color(blue)(1))#

#4x^3 + 2x^2 + 10x^2 + 5x - 6x - 3#

We can now combine like terms:

#4x^3 + (2 + 10)x^2 + (5 - 6)x - 3#

#4x^3 + 12x^2 + (-1)x - 3#

#4x^3 + 12x^2 - 1x - 3#

#4x^3 + 12x^2 - x - 3#

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