Question

How do you evaluate `(a ^ { 3} - 5a + 2) ( a ^ { 2} - a + 5)`?

Answer 1

`=a^5-a^4+7a^2-27a+10`

Explanation:

Each term in the first bracket has to be multiplied by each term in the second bracket. This will give `9` terms before simplifying them.

`(color(blue)(a^3) color(forestgreen)(-5a) color(red)(+2))(a^2 -a+5)`

`=color(blue)(a^3)(a^2 -a+5) color(forestgreen)(-5a)(a^2 -a+5) color(red)(+2)(a^2 -a+5))`

Using the distributive law gives:

`=color(blue)(a^5-a^4+5a^3)color(forestgreen)(-5a^3+5a^2-25a)color(red)(+2a^2-2a+10)`

Add like terms:

`=a^5-a^4+7a^2-27a+10`

Answer 2

`color(green)(a^5-a^4+7a^2-27a+10)`

Explanation:

`color(white)(aaaaaaaaaaaaa)` `a^3-5a+2`
`color(white)(aaaaaaaaaaa)` `xx a^2-a+5`
`color(white)(aaaaaaaaaaaaa)` `overline(a^5+0-5a^3+2a^2)`
`color(white)(aaaaaaaaaaaaa)` `0-a^4+0+5a^2-2a`
`color(white)(aaaaaaaaaaaaa)` `0+0+5a^3+0-25a+10`
`color(white)(aaaaaaaaaaaaa)` `overline(a^5-a^4+0+7a^2-27a+10`

`color(green)(a^5-a^4+7a^2-27a+10`