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

2 Answers
Mar 3, 2018

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.)

Mar 3, 2018

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.