To find the expression that represents the area of the rectangle, we need to multiply the length by the width. The length is given as [tex]\( x - 8 \)[/tex] units, and the width is given as [tex]\( x + 11 \)[/tex] units.
Let's perform the multiplication:
[tex]\[
(x - 8)(x + 11)
\][/tex]
We can apply the distributive property, often called the FOIL method (First, Outer, Inner, Last), to expand this product:
1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot x = x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
x \cdot 11 = 11x
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-8 \cdot x = -8x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-8 \cdot 11 = -88
\][/tex]
Now, add all these products together:
[tex]\[
x^2 + 11x - 8x - 88
\][/tex]
Combine the like terms ([tex]\(11x\)[/tex] and [tex]\(-8x\)[/tex]):
[tex]\[
x^2 + 3x - 88
\][/tex]
So, the expression that represents the area of the rectangle is:
[tex]\[
x^2 + 3x - 88
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x^2 + 3x - 88 \)[/tex]
