Answer:
The area of the photograph is: [tex]A=x^2-4[/tex]
Step-by-step explanation:
Given
The length of rectangular photograph = [tex]l[/tex] = (x + 2) inches
The width of rectangular photograph = [tex]w[/tex] = (x - 2) inches
To determine
The area of the photograph
Important Tip:
Given that the photograph is in the shape of a rectangle. Thus, we can use the formula involving the area of a rectangle to determine the area of a photograph.
The Area of the photograph can be determined using the formula
[tex]A = wl[/tex]
where
now substituting [tex]l = (x + 2)[/tex] and [tex]w = (x-2)[/tex] in the formula
[tex]A = wl[/tex]
[tex]A = (x-2) (x+2)[/tex]
Apply Difference of Two Squares Formula: [tex]\left(a-b\right)\left(a+b\right)=a^2-b^2[/tex]
[tex]A=x^2-2^2[/tex] ∵ [tex]a=x,\:b=2[/tex]
[tex]A=x^2-4[/tex] ∵ [tex]2^2=4[/tex]
Therefore, the area of the photograph is: [tex]A=x^2-4[/tex]
