Question

write an expression for the area of the largest rectangle on the right in two different ways. the first way to write an expression for the area of the largest rectangle is (type your answer in factored form.)

Explanation:

Step1: Identify rectangle dimensions

The length of the large - rectangle is $1 + 3x$ and the width is $x$.

Step2: Use area formula $A = lw$

The area $A$ of a rectangle is given by the product of its length $l$ and width $w$. So, the factored - form of the area is $x(1 + 3x)$.

Step3: Expand the factored form

Using the distributive property $a(b + c)=ab+ac$, where $a = x$, $b = 1$, and $c = 3x$, we get $x\times1+x\times3x=x + 3x^{2}$.

Answer:

The first way (factored form): $x(1 + 3x)$
The second way (expanded form): $x + 3x^{2}$