Question

How do you find the product of `(a+5)(a-6)`?

Answer 1

`a^2 - a - 30`

Explanation:

To solve this, we expand/distribute using FOIL:

As you can see in this image, the first thing we do is multiply the `color(steelblue)"firsts"`:
`a * a = a^2`

Then the `color(purple)"outers"`:
`a * -6 = -6a`

Then the `color(peru)"inners"`:
`5 * a = 5a`

and finally the `color(olivedrab)"lasts"`:
`5 * -6 = -30`

Now combine them all together:
`a^2 - 6a + 5a - 30`

We can still simplify the like terms. Let's color-code them:
`a^2 quadcolor(red)(-quad6a quad+quad 5a) quad - quad30`

Combine like terms and get the final answer:
`a^2 - a - 30`

Hope this helps!

Answer 2

`a^2-a -30`

Explanation:

`color(blue)((a+5))color(green)( (a-6) )`

Multiply everything in the right brackets (green) by everything in the left brackets (blue).

`color(green)(color(blue)(a)(a-6) color(white)("ddd")color(blue)(+5)(a-6) )`

Notice that the + sign followed the 5

`a^2-6acolor(white)("dd")+5a-30`

but `-6a+5a` is the same as `-a` giving.

`a^2-a -30`