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Quickly expand (a±b)² algebraic expressions into standard polynomials. Ideal for math learning and verification.
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Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Enter values for a and b; the calculator evaluates (a + b)² and displays the equation with a numeric result. Despite the page title, it does not expand a variable expression into a polynomial. Inputs are numeric fields, so entries such as x or 2x are not symbolic algebra.
The identity (a+b)² = a² + 2ab + b² explains why the result works: multiply the sum by itself. For a=3 and b=2, the calculator evaluates (3+2)² = 25; expanding by hand gives 9 + 12 + 4 = 25. OpenStax describes the binomial-square pattern, including the corresponding minus form, for algebraic work.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Enter a number in each of the a and b fields. Decimals and negative values are useful; use a negative b when you want to evaluate a difference, such as 7 + (−4).
Choose how many decimal places to display and whether non-integer results should be rounded or truncated.
Read the equation line to confirm the values and sign, then copy or record the result if needed.
Example: with a=1.2 and b=0.3, the sum is 1.5 and its square is 2.25. With a=4 and b=−1.5, the sum is 2.5 and the result is 6.25. These examples can be checked using the expanded identity, but the output remains a numeric evaluation.
Use cases
See how the tool fits into real work and everyday tasks.
Substitute particular numbers into a binomial-square expression to verify the numerical value, while keeping symbolic expansion as a separate written step.
When a spreadsheet or estimate requires the square of two values’ sum, compare the displayed result against the inputs and chosen decimal display.
Q&A
Find concise answers to common questions and confusing cases.
No. It evaluates numeric values entered for a and b; it does not preserve variables or produce x² + 6x + 9.
Enter b as a negative value. For example, a=7 and b=−4 evaluate (7 + (−4))², which is (7−4)² = 9.
Check the selected decimal-place count and display mode. Rounding and truncation can produce different displayed endings for non-integer results.
Notes
Review scope, result limitations, and important precautions before use.
The formula squares the numeric sum. Decimal-place settings format non-integer results, and the displayed value may omit extra precision. For exact fractions, symbolic variables or a full algebraic expansion, use an appropriate symbolic method and retain the exact input values.
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