Removing brackets means rewriting an expression while preserving its value. Expand using the operation outside the bracket, then combine like terms. Pay particular attention to a minus sign: subtracting a bracket changes the sign of every term inside it.
Identify the operation first
A number or expression beside a bracket usually indicates multiplication in elementary algebra. A plus sign before a bracket and a minus sign before a bracket have different effects. Read the whole expression and identify the scope of each operation before changing symbols. Do not remove brackets by simply deleting them from the written expression.
Distribute multiplication across the terms
For 3(x + 4), multiply both terms to obtain 3x + 12. In −3(2x − 5), multiplying each term gives −6x + 15. The second term is positive because the two negative signs multiply. Write the intermediate expansion if the signs are difficult to track.
Handle subtraction of a bracket
For 2x − (x − 4), subtract both terms in the bracket: 2x − x + 4. This simplifies to x + 4. Changing only the first sign would produce a different expression. Keep the bracket’s boundary clear, particularly when several groups or nested expressions occur.
Combine only like terms
Terms with the same variable part and powers can be combined through their coefficients. In −6x + 15 + 4x, the x terms combine to −2x, leaving −2x + 15. A constant and an x term are not like terms. Likewise, x and x² cannot be combined by simply adding their coefficients.
Check the result against the original
Substitute a convenient value for the variable into both forms as a check for obvious mistakes. Agreement at one value does not prove a general identity, so also review the valid algebraic steps. Keep equality signs between equivalent expressions and avoid turning a simplification task into solving an equation that was never given.
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