How do you simplify the product #(3x + 1)(4x^2 - 2x + 1)# and write it in standard form?

1 Answer
Jun 4, 2017

Answer:

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)(3x) + color(red)(1))(color(blue)(4x^2) - color(blue)(2x) + color(blue)(1))# becomes:

#(color(red)(3x) xx color(blue)(4x^2)) - (color(red)(3x) xx color(blue)(2x)) + (color(red)(3x) xx color(blue)(1)) + (color(red)(1) xx color(blue)(4x^2)) - (color(red)(1) xx color(blue)(2x)) + (color(red)(1) xx color(blue)(1))#

#12x^3 - 6x^2 + 3x + 4x^2 - 2x + 1#

We can now group and combine like terms:

#12x^3 - 6x^2 + 4x^2 + 3x - 2x + 1#

#12x^3 + (-6 + 4)x^2 + (3 - 2)x + 1#

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

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