Question

How do you multiply `(- 8x - 2) ( - 6x ^ { 2} - 4x - 8)`?

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)(-8x) - color(red)(2))(-color(blue)(6x^2) - color(blue)(4x) - color(blue)(8))` becomes:

`(color(red)(-8x) xx color(blue)(-6x^2)) + (color(red)(-8x) xx color(blue)(-4x)) + (color(red)(-8x) xx color(blue)(-8)) + (color(red)(-2) xx color(blue)(-6x^2)) + (color(red)(-2) xx color(blue)(-4x)) + (color(red)(-2) xx color(blue)(-8))`

`48x^3 + 32x^2 + 64x + 12x^2 + 8x + 16`

We can now group and combine like terms:

`48x^3 + 32x^2 + 12x^2 + 64x + 8x + 16`

`48x^3 + (32 + 12)x^2 + (64 + 8)x + 16`

`48x^3 + 44x^2 + 72x + 16`