Add polynomial expressions

Adding polynomial expressions means combining like terms—terms with the same variables raised to the same exponents—by adding their coefficients, while unlike terms remain separate. Correctly handling positive and negative coefficients, constants, and parentheses produces an equivalent expression, usually written in standard form, and reinforces the distributive, commutative, and associative properties of addition. This understanding supports simplifying algebraic expressions, solving equations, and later factoring; abstract polynomial algebra and operations involving more advanced coefficient systems are not included.

Detailed Explanation: Add polynomial expressions

Like terms have the same variables raised to the same exponents. To add polynomial expressions:

Remove parentheses, keeping each term’s sign.
Group like terms.
Add their coefficients.
Write the result in standard form, with highest exponents first.

Example

Simplify:

(3x^2-5x+7)+(-x^2+2x-4)

Step 1: Remove the parentheses.

Because the expressions are being added, each term keeps its sign:

3x^2-5x+7-x^2+2x-4

Step 2: Group like terms.

(3x^2-x^2)+(-5x+2x)+(7-4)

Step 3: Add the coefficients of each group.

2x^2-3x+3

Therefore,

\boxed{(3x^2-5x+7)+(-x^2+2x-4)=2x^2-3x+3}

Notice that $x^2$ terms combine with $x^2$ terms, $x$ terms combine with $x$ terms, and constants combine with constants. Unlike terms, such as $x^2$ and $x$ , cannot be combined.

Learn by doing: Add polynomial expressions

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Like Terms - Combine - Order N - Whole - One Variable - Expression to Pair

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