1. **State the problem:** We need to find expressions for A, B, and C in the algebraic sums given. 2. **Recall the example:** - $2a + 3a = 5a$ - $4a + 7a = 12a$ This shows that like terms (same variable) are added by summing their coefficients. 3. **Given expressions:** - First sum: $4k + 6n + 2k + 3n + A$ - Second sum: $B + 5k + 7n$ - Third sum: $C$ 4. **Find B:** Combine like terms in the first sum except $A$: $$4k + 2k = 6k$$ $$6n + 3n = 9n$$ So, $$B = 6k + 9n$$ 5. **Find C:** Add $B$ and $5k + 7n$: $$B + 5k + 7n = (6k + 9n) + 5k + 7n = (6k + 5k) + (9n + 7n) = 11k + 16n$$ So, $$C = 11k + 16n$$ 6. **Find A:** $A$ is the sum of the entire expression, which is $4k + 6n + 2k + 3n + 5k + 7n$. Combine all like terms: $$4k + 2k + 5k = 11k$$ $$6n + 3n + 7n = 16n$$ So, $$A = 11k + 16n$$ **Final answers:** - $A = 11k + 16n$ - $B = 6k + 9n$ - $C = 11k + 16n$