To determine which expression represents the area of the rectangle with the given length and width, we need to multiply these two terms together. Let's go step-by-step to find the product:
1. Write down the expressions for the length and width of the rectangle.
- Length: [tex]\( (x - 8) \)[/tex]
- Width: [tex]\( (x + 11) \)[/tex]
2. The formula for the area of a rectangle is:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
3. Substitute the given expressions for the length and width:
[tex]\[
\text{Area} = (x - 8) \times (x + 11)
\][/tex]
4. Use the distributive property (also known as the FOIL method for binomials) to expand the product:
[tex]\[
(x - 8) \times (x + 11) = x \cdot x + x \cdot 11 - 8 \cdot x - 8 \cdot 11
\][/tex]
5. Simplify the terms individually:
[tex]\[
x \cdot x = x^2
\][/tex]
[tex]\[
x \cdot 11 = 11x
\][/tex]
[tex]\[
-8 \cdot x = -8x
\][/tex]
[tex]\[
-8 \cdot 11 = -88
\][/tex]
6. Combine all these terms together:
[tex]\[
x^2 + 11x - 8x - 88
\][/tex]
7. Simplify by combining like terms:
[tex]\[
x^2 + (11x - 8x) - 88
\][/tex]
[tex]\[
x^2 + 3x - 88
\][/tex]
Therefore, the expression that represents the area of the rectangle is:
C. [tex]\( x^2 + 3x - 88 \)[/tex]
