Question

How do you multiply `(2x + 7) ( 7x ^ { 2} - 8x + 6)`?

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)(2x) + color(red)(7))(color(blue)(7x^2) - color(blue)(8x) + color(blue)(6))` becomes:

`(color(red)(2x) xx color(blue)(7x^2)) - (color(red)(2x) xx color(blue)(8x)) + (color(red)(2x) xx color(blue)(6)) + (color(red)(7) xx color(blue)(7x^2)) - (color(red)(7) xx color(blue)(8x)) + (color(red)(7) xx color(blue)(6))`

`14x^3 - 16x^2 + 12x + 49x^2 - 56x + 42`

We can now group and combine like terms:

`14x^3 - 16x^2 + 49x^2 + 12x - 56x + 42`

`14x^3 + (-16 + 49)x^2 + (12 - 56)x + 42`

`14x^3 + 33x^2 + (-44)x + 42`

`14x^3 + 33x^2 - 44x + 42`