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