Which of the following represents the area of a rectangle whose length is [tex]5x - 3[/tex] and whose width is [tex]x + 7[/tex]?

A. [tex]5x^2 - 21[/tex]
B. [tex]5x^2 + 9x - 21[/tex]
C. [tex]5x^2 + 32x - 21[/tex]
D. [tex]5x^2 - 32x - 21[/tex]



Answer :

To find the area of a rectangle, we need to multiply its length by its width. Given the length [tex]\(5x - 3\)[/tex] and the width [tex]\(x + 7\)[/tex], we can find the area by following these steps:

1. Write the expression for the area of the rectangle, which is the product of its length and width:

[tex]\[ \text{Area} = (5x - 3) \cdot (x + 7) \][/tex]

2. Perform the multiplication by using the distributive property (i.e., multiplying each term in the first expression by each term in the second expression):

[tex]\[ (5x - 3) \cdot (x + 7) = 5x \cdot x + 5x \cdot 7 - 3 \cdot x - 3 \cdot 7 \][/tex]

3. Simplify each term obtained from the distribution:

[tex]\[ = 5x \cdot x + 5x \cdot 7 - 3 \cdot x - 3 \cdot 7 \][/tex]
[tex]\[ = 5x^2 + 35x - 3x - 21 \][/tex]

4. Combine the like terms (i.e., terms that contain [tex]\(x\)[/tex]):

[tex]\[ = 5x^2 + (35x - 3x) - 21 \][/tex]
[tex]\[ = 5x^2 + 32x - 21 \][/tex]

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

[tex]\[ 5x^2 + 32x - 21 \][/tex]

Among the given choices, the correct answer is:

[tex]\[ 5x^2 + 32x - 21 \][/tex]