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). x^2 + 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 (x + 5)(x + 1). (type your answer in factored form.)
c. are the pieces in figures (a) and (b) the same? what factorization is illustrated? set the expressions that are obtained in parts (a) and (b) equal to each other. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
yes, the pieces in figures (a) and (b) are the same. thus, the equation is
a. (use integers or fractions for any numbers in the equation.)
b. no, the pieces in figures (a) and (b) are different.

Explanation:

Step1: Analyze figure (a) area

The area of the square is $x^2$, there are 6 rectangles with area $x$ and 5 unit - squares. So the sum of areas is $x^2 + 6x+5$.

Step2: Analyze figure (b) area

The length of the rectangle in figure (b) is $x + 5$ and the width is $x + 1$. So the area is $(x + 5)(x + 1)$.

Step3: Compare figures

The pieces in figures (a) and (b) are the same. We set the two expressions equal: $x^2+6x + 5=(x + 5)(x + 1)$.

Answer:

A. $x^2+6x + 5=(x + 5)(x + 1)$