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Select the correct answer.

The length of a rectangle is [tex]\((x - 8)\)[/tex] units, and its width is [tex]\((x + 11)\)[/tex] units. Which expression can represent the area of the rectangle?

A. [tex]\(x^2 + 3x + 88\)[/tex]
B. [tex]\(x^2 - 3x - 88\)[/tex]
C. [tex]\(x^2 + 3x - 88\)[/tex]
D. [tex]\(x^2 - 3x + 88\)[/tex]


Sagot :

To determine the area of the rectangle, we need to multiply its length by its width. The length of the rectangle is given as [tex]\(x - 8\)[/tex] units, and the width is given as [tex]\(x + 11\)[/tex] units.

So, the area [tex]\(A\)[/tex] can be represented as:

[tex]\[ A = \text{length} \times \text{width} = (x - 8)(x + 11) \][/tex]

We'll expand this expression step-by-step to find the area in its simplified form.

First, we'll use the distributive property (also known as the FOIL method for binomials) to expand the expression:

[tex]\[ (x - 8)(x + 11) = x(x + 11) - 8(x + 11) \][/tex]

Distribute [tex]\(x\)[/tex] in the first term:

[tex]\[ x(x + 11) = x^2 + 11x \][/tex]

Distribute [tex]\(-8\)[/tex] in the second term:

[tex]\[ -8(x + 11) = -8x - 88 \][/tex]

Now, combine these two results:

[tex]\[ x^2 + 11x - 8x - 88 \][/tex]

Combine like terms:

[tex]\[ x^2 + (11x - 8x) - 88 \][/tex]

Simplify:

[tex]\[ x^2 + 3x - 88 \][/tex]

Thus, the expression that represents the area of the rectangle is:

[tex]\[ x^2 + 3x - 88 \][/tex]

So, the correct answer is:

[tex]\[ \boxed{x^2 + 3x - 88} \][/tex]

This corresponds to option C.
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