1. **State the problem:** We have a tree structure where expressions are added stepwise. On the right side, we want to find expressions $A$, $B$, and $C$ such that: - $A$ is added to $2x + 3y$. - $B$ is the sum of $6x + 2y$ and $2x + 3y$. - $C$ is the sum of $B$ and $7x + 6y$. 2. **Find $B$:** $$B = (6x + 2y) + (2x + 3y)$$ Add like terms: $$B = (6x + 2x) + (2y + 3y) = 8x + 5y$$ 3. **Find $C$:** $$C = B + (7x + 6y) = (8x + 5y) + (7x + 6y)$$ Add like terms: $$C = (8x + 7x) + (5y + 6y) = 15x + 11y$$ 4. **Find $A$:** From the diagram, $A$ is added to $2x + 3y$ to get $7x + 6y$: $$A + (2x + 3y) = 7x + 6y$$ Subtract $2x + 3y$ from both sides: $$A = (7x + 6y) - (2x + 3y)$$ Show cancellation: $$A = \cancel{7x} + 6y - \cancel{2x} - 3y$$ Simplify: $$A = (7x - 2x) + (6y - 3y) = 5x + 3y$$ **Final answers:** $$A = 5x + 3y$$ $$B = 8x + 5y$$ $$C = 15x + 11y$$