Combine like terms informally

Like terms represent the same variable quantity, such as $x$ and $x$ , so their coefficients can be added or subtracted while the variable part remains unchanged; constants combine with constants (for example, $3x+2x+4+1=5x+5$ ). This preserves an equivalent value for every substitution and distinguishes terms that cannot be combined, such as $x$ and $y$ or $x$ and $x^2$ , without extending to more advanced polynomial rules.

Detailed Explanation: Combine like terms informally

Like terms have the same variable part. For example, $x$ and $x$ are like terms, and constants such as $4$ and $1$ are also like terms. Terms with different variables, such as $x$ and $y$ , cannot be combined.

Example: Simplify

3x+4+2x+1

Step 1: Find the like terms.

$3x$ and $2x$ are like terms.
$4$ and $1$ are constants, so they are like terms.

Step 2: Combine the coefficients of the $x$ terms.

The coefficient of $3x$ is $3$ , and the coefficient of $2x$ is $2$ :

3x+2x=5x

Keep the variable $x$ unchanged.

Step 3: Combine the constants.

4+1=5

Step 4: Write the simplified expression.

\boxed{5x+5}

So, $3x+4+2x+1$ is equivalent to $5x+5$ .

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Algebraic Functions - Multiply Bracketed Terms, Same Variable

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Combine like terms informally

Detailed Explanation: Combine like terms informally

Learn by doing: Combine like terms informally

Practice with unlimited practice problems

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Algebraic Functions - Multiply Bracketed Terms, Same Variable