1. **State the problem:** We need to expand the expression $$(x + y)(x + 6y)$$ which represents the area of a rectangle with length $(x + y)$ and width $(x + 6y)$. 2. **Formula used:** To expand the product of two binomials, we use the distributive property (also known as FOIL method for binomials): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x + y)(x + 6y) = x \cdot x + x \cdot 6y + y \cdot x + y \cdot 6y $$ 4. **Simplify each term:** $$ = x^2 + 6xy + xy + 6y^2 $$ 5. **Combine like terms:** $$ 6xy + xy = 7xy $$ 6. **Final expanded expression:** $$ x^2 + 7xy + 6y^2 $$ This expression represents the area of the rectangle in terms of $x$ and $y$.