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]
