Question

the total area of two rectangles can be represented by the expression $(x)(3x + 1) + (2x)(x + 3)$.
which expression represents the total area of the two rectangles?
$\boldsymbol{\text{a}}\\ 7x^2$
$\boldsymbol{\text{b}}\\ 6x^2 + 6x$
$\boldsymbol{\text{c}}\\ 6x^2 + 7x$
$\boldsymbol{\text{d}}\\ 5x^2 + 7x$

Explanation:

Step1: Expand each product

First, expand \((x)(3x + 1)\):
Using the distributive property (\(a(b + c)=ab + ac\)), we get \(x\cdot3x + x\cdot1 = 3x^2 + x\).

Next, expand \((2x)(x + 3)\):
Using the distributive property, we get \(2x\cdot x + 2x\cdot3 = 2x^2 + 6x\).

Step2: Add the expanded expressions

Now, add the two expanded expressions:
\((3x^2 + x) + (2x^2 + 6x)\).

Combine like terms:
For \(x^2\) terms: \(3x^2 + 2x^2 = 5x^2\).
For \(x\) terms: \(x + 6x = 7x\).

So the total area is \(5x^2 + 7x\).

Answer:

d) \(5x^2 + 7x\)