(x+4)^2 can be expressed as (x+4)*(x+4). Then, just FOIL.

x^2+8x+16

In the second question, you’re looking for the number to complete the perfect square, so that the equation looks like the one above. So, what number when added to itself equals 10? This equation would look like:

y+y=10

That’s easy to solve:

2y=10

y=5

So, that means our original formula looked like:

(b+5)^2

Now, foil again to see if our problem is right:

(b+5)(b+5)

b^2+10b+25

So, the term to be added is 25

1. (x+4)(x+4) = x^2 + 8x + 16

2. b^2 + 10b + 25 = (b+5)(b+5)

Have you ever heard of FOIL? Or Quadratic Equations?

The first problem should be set-up

(x+4)(x+4) = x^2 + 8x = 16

The second is

b^2 + 10b + 25