Given:
Dimensions of lot is (7+x) and (7-x).
Dimension of house is (3+x) and (3-x)
Taylor is thinking about extending the house by adding 3 feet to the length and width.
So, the dimension of house becomes (6+x) feet and (6-x) feet.
Now, the area of the yard is,
[tex]\begin{gathered} \text{Yard}=\text{area of the lot-area of the house} \\ =(7+x)(7-x)-(6+x)(6-x) \\ =49-x^2-(36-x^2) \\ =49-36-x^2+x^2 \\ =13\text{ square f}eet \end{gathered}[/tex]
Answer: area for the yard left is 13 square feet.
