Adding polynomials means combining like terms—terms with the same variables raised to the same powers—by adding their coefficients, while retaining unlike terms separately and preserving constants. The understanding includes interpreting addition as combining algebraic quantities, rewriting results in standard form, and managing negative coefficients and parentheses through integer addition; polynomial multiplication, division, and more abstract generalizations are outside this scope.
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Detailed Explanation: Add polynomials
To add polynomials, combine like terms. Like terms have the same variable raised to the same power. Add their coefficients and keep the variable part unchanged.
Example:
Step 1: Remove the parentheses.
Because a plus sign comes before the second polynomial, all signs stay the same:
Step 2: Group like terms.
Step 3: Add the coefficients.
So the sum is:
Write the answer in standard form, with terms arranged from the greatest exponent to the smallest. Terms that are not alike, such as and , cannot be combined.
Learn by doing: Add polynomials
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Like Terms - Combine - Order 2 - Fractional - One Variable - Expression to Pair
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Download/Modify Free Grade 9 'Add polynomials' Worksheet
Print this free 'Add polynomials' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Like Terms - Combine - Order 2 - Fractional - One Variable - Expression to Pair
- Like Terms - Combine - Order 2 - Whole - One Variable - Expression to Pair
- Like Terms - Combine - Order N - Whole - One Variable - Expression to Pair
- Like Terms - Combine - Order N - Fractional - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order N - Whole - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order 2 - Fractional - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order 1 - Fractional - Multiple Variables - Expression to Pair
- Like Terms - Combine - Order 1 - Whole - Multiple Variables - Expression to Pair
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