Question

consider the given figures (a) and (b). answer parts a through c.
a. write a trinomial that expresses the sum of the areas of the twelve rectangular pieces shown in figure (a).
x² + 6x + 5
(use integers or fractions for any numbers in the expression. do not factor.)
b. express the area of the large rectangle in figure (b) as the product of two binomials.
the area of the large rectangle in figure (b) expressed as the product of its length times width is
(type your answer in factored form.)

Explanation:

Step1: Identify length and width

The length of the large - rectangle in figure (b) is \(x + 5\) and the width is \(x+1\).

Step2: Use area formula

The area \(A\) of a rectangle is \(A=\text{length}\times\text{width}\). So, \(A=(x + 5)(x + 1)\).

Answer:

\((x + 5)(x + 1)\)