Final answer:
The exercise involves matching algebraic expressions to their simplified results through basic operations such as addition and subtraction. Some expressions simplify directly by combining like terms, while others require subtraction or addition of polynomials. The correct matches are A with B, C with H, D with G, E with F, and J as it stands.
Step-by-step explanation:
The task is to match each algebraic sum or difference with its answer. First, let's simplify each expression:
- For A, x^4 + 6x - 10x simplifies to x^4 - 4x, because you combine like terms (6x - 10x = -4x).
- For B, 2x^4 + 3x - 5x simplifies to 2x^4 - 2x, also by combining like terms (3x - 5x = -2x).
- For C, nothing changes as there is no like term in 9x^4 - 3x^3 + 12x + 1.
- For D, we perform subtraction: (10x^4 - 5) - (9x^3 + 2x) results in 10x^4 - 9x^3 - 2x - 5.
- For E, the subtraction is (15x^3 + 12x + 1) - (6x + 5x + 2), which simplifies to 15x^3 + x - 1.
- For F, the subtraction (2x^4 - 2x) - (-4x^3 + 3x) gives 2x^4 + 4x^3 - 5x.
- For G, (9x^3 + 2x) + (10x^4 - 5) yields 10x^4 + 9x^3 + 2x - 5, by adding like terms.
- For H, (9x^4 + 10x) + (3x^3 + 2x + 1) simplifies to 9x^4 + 3x^3 + 12x + 1.
- For I, (x + 3x - 5x) + (x + 3x - 5x) results in -8x.
- For J, 9x + 3x - 1 simplifies to 12x - 1.
- For K and L, these are just the negative of one another and cannot be simplified any further based on the given expressions.
Therefore, the correct match-ups are A with B, C with H, D with G, E with F, and J remains correct as provided.