Question

What is the product of `d-9` and `2d^2+11d-4`?

Answer 1

`2d^3-7d^2-103d+36`

Explanation:

`(color(magenta)dcolor(lime)(-9))xxcolor(blue)(""(2d^2+11d-4))`

using the distributive property:
`color(white)("XXX")=color(magenta)dcolor(blue)(""(2d^2+11d-4))color(lime)(-9)color(blue)(""(2d^2+11d-4))`

expanding the individual terms (by multiplying):
`color(white)("XXX")=color(magenta)(2d^3+11d^2-4d)color(lime)(-18d^2-99d+36)`

combining like terms:
`color(white)("XXX")=2d^3-7d^2-103d+36`

Answer 2

`=2d^3-7d^2-103d+36`

Explanation:

`d*(2d^2+11d-4)-9*(2d^2+11d-4)`
`=2d^2*d+11d*d-4*d-2d^2*9-11d*9+4*9`
`=2d^3+11d^2-4d-18d^2-99d+36`
`=2d^3-7d^2-103d+36`