Add, subtract, and multiply polynomials.
Polynomial arithmetic follows the same rules as regular arithmetic—you just need to track each term carefully through distribution and combination.
核心知识
When adding or subtracting polynomials, combine like terms. When multiplying, distribute every term in the first polynomial to every term in the second, then combine like terms in the result.
深入理解
Adding polynomials is straightforward: drop the parentheses and combine like terms. Subtraction is where errors happen—the minus sign distributes to every term in the second polynomial, not just the first.
Multiplying polynomials requires each term in one factor to multiply each term in the other. For two binomials, FOIL (First, Outer, Inner, Last) works as a checklist. For larger polynomials, take each term of the first polynomial and multiply it through the entire second polynomial, then combine all like terms.
A useful check: multiplying a polynomial with
分步讲解
- If adding: remove parentheses and combine like terms.
- If subtracting: distribute the negative sign to every term in the second polynomial, then combine like terms.
- If multiplying: multiply each term of the first polynomial by every term of the second.
- Collect and combine all like terms.
- Write the result in standard form (descending degree).
常见误解
- When subtracting polynomials, only negating the first term of the second polynomial instead of every term.
- When multiplying, missing cross terms—especially the middle products in larger expansions.
- Confusing addition with multiplication: trying to multiply coefficients of like terms instead of adding them.
示例解析
Which polynomial is equivalent to
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