Apiece of wire 5 inches long is to be cut in two pieces. one piece is x inches long and is to be bent into the shape of a square. the other piece is to be bent in the shape of a circle. find an expression for the total area made up by the square and the circle as a function of x.

Check the picture below.

since, we know that for the circle, the perimeter is s+s+s+s or 4s, then 4s = x and so on.

now, for the circle, the perimeter is just the circumference, circumference of a circle is 2πr, thus 2πr = 5-x and so on.

anyway... so... the equation of the area made by those two in x-terms, is just their sum... so let's do that then



now, you can expand the squared binomial on the numerator, but there will not be any like-terms to simplify, so, it won't make much difference, so.... you can expand it or not.