Question

(n+5) (n+4) = ?? someone help thank yoh

Answer 1

The result is `n^2+9n+20`.

Explanation:

You can use the distributive property twice. First, distribute `(n+5)` onto `n`, and then onto `4`, like this:

`color(white)=color(blue)((n+5))color(red)((n+4))`

`=color(blue)((n+5))color(red)n+color(blue)((n+5))color(red)4`

`=color(red)ncolor(blue)((n+5))+color(red)4color(blue)((n+5))`

Now, use the distributive in each of these smaller parts:

`color(white)=color(red)ncolor(blue)((n+5))+color(red)4color(blue)((n+5))`

`=color(red)ncolor(blue)n+color(red)ncolor(blue)5+color(red)4color(blue)((n+5))`

`=color(purple)(n^2)+color(blue)5color(red)n+color(red)4color(blue)((n+5))`

`=color(purple)(n^2)+color(blue)5color(red)n+color(red)4color(blue)n+color(red)4*color(blue)5`

`=color(purple)(n^2)+color(blue)5color(red)n+color(red)4color(blue)n+color(purple)20`

Lastly, combine the like terms:

`color(white)=color(purple)(n^2)+color(blue)5color(red)n+color(red)4color(blue)n+color(purple)20`

`=color(purple)(n^2)+color(purple)(9n)+color(purple)20`

This is the result. (It is called a quadratic.)

Answer 2

`color(red)(n^2)+color(blue)9color(red)n+color(blue)20`

Explanation:

To solve this, we must multiply each variable in one bracket by each variable in the other brackets.

This is called distributing:

`(color(red)n+color(blue)5)(color(red)n+color(blue)4)`

becomes:

`(color(red)n*color(red)n)+(color(red)n*color(blue)4)+(color(red)n*color(blue)5)+(color(blue)5*color(blue)4)`

`=color(red)(n^2)+color(blue)4color(red)n+color(blue)5color(red)n+color(blue)20`

Simplifying:

`->color(red)(n^2)+color(blue)9color(red)n+color(blue)20`

Thus, solved.