Question

How do you multiply `(2r^2+5r-1)(5r^2+2r-8)`?

Answer 1

`10r^4+29r^3-11r^2-42r+8`

Explanation:

`"each term in the second factor is multiplied by each term"`
`"in the first factor"`

`=(color(red)(2r^2+5r-1))(5r^2+2r-8)`

`=color(red)(2r^2)(5r^2+2r-8)color(red)(+5r)(5r^2+2r-8)`
`color(white)(=)color(red)(-1)(5r^2+2r-8)`

`"distributing gives"`

`=10r^4+4r^3-16r^2+25r^3+10r^2-40r-5r^2-2r+8`

`"collecting like terms"`

`=10r^4+29r^3-11r^2-42r+8`