Question

Use the information given to answer the question.

Consider the rectangle.




Part A


If the area of the rectangle is represented by the expression

(

x

−

3

)

(

x

+

3

)

square units, which expression represents an equivalent area?



(

x

2

−

9

)

square units


( x 2 − − 9 ) square units


(

x

2

−

6

x

+

9

)

square units


( x 2 − − 6 x + 9 ) square units


(

x

2

+

6

x

−

9

)

square units


( x 2 + 6 x − − 9 ) square units


(

x

2

+

9

)

square units

Answer 1

Area is (x² - 9) units squared.

Explanation:

• from difference of squares quadratic property:

`{ \boxed{ \rm{(a - b)(a + b) = ( {a}^(2) - {b}^(2)) }}}`

→ a is x

→ b is 3

• Therefore:

`{ \tt{area = {x}^(2) - {3}^(2) }} \\ \\ { \tt{area = {x}^(2) - 9 }}`