Question

How do you multiply polynomials `(a + 3)(a - 2)`?

Answer 1

`a^2+a-6`

Explanation:

`a*a=a^2`

`a*-2=-2a`

`3*a=3a`

`3*-2=-6`

Now when we combine them all together we get:

`a^2-2a+3a-6`

We still need to simplify this since `-2a` and `3a` are like terms. So the final answer is:
`a^2+a-6`

Hope this helps!

Answer 2

`a^2+a-6`

Explanation:

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

`rArr(color(red)(a+3))(a-2)`

`=color(red)(a)(a-2)color(red)(+3)(a-2)larrcolor(blue)"distribute"`

`=(color(red)(a)xxa)+(color(red)(a)xx-2)+(color(red)(3)xxa)+(color(red)(3)xx-2)`

`=a^2color(blue)(-2a)color(blue)(+3a)-6larrcolor(blue)"collect like terms"`

`=a^2color(blue)(+a)-6`

`rArr(a+3)(a-2)=a^2+a-6`