Calculate the algebraic expansion of (a+b)³ and (a-b)³. Supports numbers and expressions, and automatically simplifies the result.
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Manually expanding (a+b)³ or (a-b)³ often leads to missing terms or miscalculated coefficients. This tool is specifically designed to solve polynomial cube expansion challenges, automatically outputting the simplified standard expanded form based on your algebraic input. Perfect cube expansion is a special form of polynomial multiplication, referring to expanding the cube of a binomial (a±b)³ into the standard polynomial expression: a³ ± 3a²b + 3ab² ± b³.
What terms are included in the perfect cube expansion result?
The standard expansion is a four-term polynomial: a³ ± 3a²b + 3ab² ± b³. The plus or minus signs depend on whether you select (a+b)³ or (a-b)³.
What should I pay attention to when entering fractions or negative numbers?
For fractions, it is recommended to use a slash (e.g., 1/2). Negative numbers must include a minus sign. Note that in (a-b)³, if 'b' is a negative number, it effectively becomes an addition cube. For instance, if b=-2, it is equivalent to (a+2)³.
Please use basic mathematical operators for input and avoid special characters. The results are only applicable to binomial cube expansions and do not support polynomials with three or more terms. All calculations are performed locally in your browser, ensuring zero risk of data upload.
For algebraic expressions with coefficients, it is recommended to use parentheses to clarify the order of operations, such as (2x) instead of 2x. A typical example: (2x+3y)³ = 8x³ + 36x²y + 54xy² + 27y³, where coefficients are calculated according to the binomial theorem. In educational settings, this tool can be used to verify manual expansion results and deepen the understanding of polynomial multiplication.
