How do you multiply # (5x-3)(x^3-5x+2)#?

1 Answer
Jun 9, 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)(5x) - color(red)(3))(color(blue)(x^3) - color(blue)(5x) + color(blue)(2))# becomes:

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

#5x^4 - 25x^2 + 10x - 3x^3 + 15x - 6#

We can now group and combine like terms:

#5x^4 - 3x^3 - 25x^2 + 10x + 15x - 6#

#5x^4 - 3x^3 - 25x^2 + (10 + 15)x - 6#

#5x^4 - 3x^3 - 25x^2 + 25x - 6#