Question

PHOTOGRAPHY A photo is$x+\mathbf{6}$ inches by$x-\mathbf{6}$ inches. What is the area of the photo?

Short answer

The area of the photo is $x^2-\mathbf{36}$.

Step-by-step solution

Step 1. Write formula for area of photo.

Area of rectangle is given by $A=\text{length}\left(l\right)\times \text{width}\left(w\right)$. Area pf photo is

$A=\left(x+6\right)\left(x-6\right)$

Step 2. Write a pattern of product of sum and difference.

The product of$x+y$ and$x-y$ is the square of x minus square of y, that is,

$$\begin{gathered} \left(x+y\right)\left(x-y\right)=\left(x-y\right)\left(x+y\right) \\ =x^2-y^2 \end{gathered}$$

Step 3. Apply pattern of product of sum and difference.

Apply the pattern of product of sum and difference to the given expression.

${\left(x\right)}^2-{\left(6\right)}^2$

Step 4. Simplify.

Simplify the above obtained expression.

$x^2-36$

Therefore, the area of the photo is $x^2-36$.