Question

How do you simplify the product `(x + 6)(x^2 - 4x + 3)` and write it in standard form?

Answer 1

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)(x) + color(red)(6))(color(blue)(x^2) - color(blue)(4x) + color(blue)(3))` becomes:

`(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(4x)) + (color(red)(x) xx color(blue)(3)) + (color(red)(6) xx color(blue)(x^2)) - (color(red)(6) xx color(blue)(4x)) + (color(red)(6) xx color(blue)(3))`

`x^3 - 4x^2 + 3x + 6x^2 - 24x + 18`

Next, group like term in descending order by the power of there exponents:

`x^3 + 6x^2 - 4x^2 + 3x - 24x + 18`

We can now combine like terms:

`x^3 + (6 - 4)x^2 + (3 - 24)x + 18`

`x^3 + 2x^2 + (-21)x + 18`

`x^3 + 2x^2 - 21x + 18`