Skill: Combine like terms

Explanation and Free Practice Resources

Combining like terms means recognizing terms with identical variable parts and exponents, then adding or subtracting their numerical coefficients while preserving the common factor; constants combine with constants, but unlike terms such as $3x$ and $2y$ cannot be combined. This use of the distributive, associative, and commutative properties produces an equivalent, simpler expression with integer or rational coefficients and supports solving equations; multiplying or factoring polynomials is beyond this scope.

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Detailed Explanation: Combine like terms

Terms are like terms when they have exactly the same variable parts and exponents. Their numerical coefficients can be combined. Constants are like terms with no variables.

For example, simplify:

7x+3y-4+2x-y+9

Step 1: Identify the like terms.

$7x$ and $2x$ are like terms.
$3y$ and $-y$ are like terms. Remember, $-y$ means $-1y$ .
$-4$ and $9$ are constants, so they are like terms.
Terms involving $x$ , $y$ , and no variable cannot be combined with one another.

Step 2: Group the like terms.

\left(7x+2x\right)+\left(3y-y\right)+\left(-4+9\right)

Step 3: Combine the coefficients.

9x+2y+5

So, the simplified expression is:

\boxed{9x+2y+5}

The variable parts stay the same while their coefficients are added or subtracted.

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Like Terms - Combine - Order 2 - Fractional - One Variable - Expression to Pair

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