Q17. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

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 $x^2-36$.