Question

find an expression for the total area of the rectangle in factored form. area = enter your next step here

Explanation:

Step1: Find the sum of the four - part areas

The four areas of the sub - rectangles are $x^{2}$, $7x$, $6x$, and $42$. The total area $A=x^{2}+7x + 6x+42$.

Step2: Combine like terms

$A=x^{2}+(7x + 6x)+42=x^{2}+13x + 42$.

Step3: Factor the quadratic expression

We need to find two numbers that multiply to $42$ and add up to $13$. The numbers are $6$ and $7$. So $x^{2}+13x + 42=(x + 6)(x+7)$.

Answer:

$(x + 6)(x + 7)$