Answer:
Let's start by assigning a variable to the original side length of the square photograph. We'll use g to represent this length.
According to the problem, each side of the new photograph will be 1 inch more than twice the original side length g. This means that the new side length will be:
2g + 1
Since this is a square photograph, all four sides are equal in length. Therefore, the area of the new photograph can be represented by the square of the new side length:
(2g + 1)^2
To simplify this expression, we can use FOIL (First, Outer, Inner, Last) to expand the squared binomial:
(2g + 1)^2 = (2g + 1)(2g + 1)
= 4g^2 + 2g + 2g + 1
= 4g^2 + 4g + 1
So the trinomial that represents the area of the enlarged photograph is:
4g^2 + 4g + 1
To check our work, we can plug in a value for g and compare the areas of the original and enlarged photographs. For example, if g = 2 (meaning the original side length is 2 inches), then the area of the original photograph is:
2^2 = 4 square inches
And the area of the enlarged photograph is:
4(2)^2 + 4(2) + 1 = 25 square inches
This makes sense, since the new photograph has sides of length 2(2) + 1 = 5 inches, and therefore an area of 5^2 = 25 square inches, which is indeed 1 inch more than twice the original area of 4 square inches.