#### Answer

The area of the expanded garage can be given by the expression $A = x^2 + 50x + 600$ $yd^{2}$.

#### Work Step by Step

The formula for the area of a rectangle, which is represented by the diagram of the garage, is given by the formula:
$$A = lw$$
According to the diagram presented and the information that the expanded garage length will be increased by $x$, the expanded length of the garage can be given by the following expression:
$$l = x + 30$$
Also according to the diagram and the information that the expanded garage width will also be increased by the amount $x$, the width is given by the following expression:
$$w = x + 20$$
With these expressions, we can plug these in for $l$ and $w$ into the equation for the area of a rectangle:
$$A = (x + 30)(x + 20)$$
We can use the FOIL method to multiply the two binomials together and expand the expression. In the FOIL method, we first multiply the first terms, then the outside terms, then the inside terms, and, finally, the last terms:
$$A = (x)(x) + (20)(x) + (30)(x) + (30)(20)$$
Now, we multiply to simplify:
$$A = x^2 + 20x + 30x + 600$$
Combine like terms to simplify the equation:
$$A = x^2 + 50x + 600$$