Question

length by the width. (x + 6) ft 3 ft use the distributive property to write two equivalent expressions for the area of the rectangle. enter the correct answers in the boxes. show hints expression: ( + ) expression: + ( )

Explanation:

Step1: Apply the distributive property

The formula for the area of a rectangle is \(A = \text{length}\times\text{width}\). Here, length \(l=(x + 6)\) ft and width \(w = 3\) ft. By the distributive property \(a(b + c)=ab+ac\), where \(a = 3\), \(b=x\), and \(c = 6\).

$$3(x+6)=3\times x+3\times6$$

Step2: Calculate the products

$$3\times x=3x$$

and

$$3\times6 = 18$$

Answer:

Expression: \(3x+18\); Expression: \(3(x + 6)\)