Certainly! To find the area of a rectangular yard, we need to multiply its length by its width. The length of the yard is given as \(\( 4x - 1 \)\) and the width is \(\( 2x + 7 \)\).
Let's calculate the area step by step:
1. Write down the expressions for the length and width:
- Length \(\( L = 4x - 1 \)\)
- Width \(\( W = 2x + 7 \)\)
2. Set up the expression for the area \(\( A \)\) of the rectangle:
- The area \(\( A \)\) is given by the product of the length and the width:
\(\[
A = L \times W
\]\)
3. Substitute the expressions for \(\( L \)\) and \(\( W \)\) into the area formula:
\(\[
A = (4x - 1) \times (2x + 7)
\]\)
4. Expand the expression:
- This can be done using the distributive property (also known as the FOIL method for binomials):
\(\[
A = (4x - 1)(2x + 7)
\]\)
So the area of the rectangular yard can be expressed as:
\(\[
(2x + 7)(4x - 1)
\]\)
Therefore, the area of the yard given the length \(\( 4x - 1 \)\) and the width \(\( 2x + 7 \)\) is \(\( (2x + 7)(4x - 1) \)\).
