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FOIL Binomial Expansion Calculator — result sheet
Expand two linear binomials, return the normalized quadratic coefficients, discriminant, and real or complex roots when the product is treated as an equation equal to zero.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: (ax+b)(cx+d)=acx²+(ad+bc)x+bd. The discriminant of the expanded quadratic is Δ=B²−4AC.
FOIL is a memory aid for the four products in two binomials: first, outer, inner, and last. This calculator shows those products as one normalized polynomial and then treats that polynomial as an optional quadratic equation for root checking.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First coefficient a — minimum -1000000; maximum 1000000
- First constant b — minimum -1000000; maximum 1000000
- Second coefficient c — minimum -1000000; maximum 1000000
- Second constant d — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| First coefficient a | 2 |
| First constant b | 3 |
| Second coefficient c | 1 |
| Second constant d | -4 |
(2x+3)(x−4)=2x²−5x−12; discriminant = 121; roots = 4 and −1.5.
Assumptions and limits
- The variable is x and both factors are linear expressions of the form coefficient × x plus constant.
- The coefficients are finite real numbers and the result is normalized by collecting like powers.
- If the leading coefficient is zero, the product reduces to a linear or constant expression and the quadratic root formula is not applied.
- A negative discriminant is reported with a complex-conjugate root pair rather than discarded.
- The calculator expands an expression; it does not factor an arbitrary polynomial entered as text.
- Floating-point output can contain ordinary decimal rounding for large or very small coefficients.
- Roots describe the equation expanded polynomial = 0, not the value of the product at a chosen x.
- Symbolic variables other than x, inequalities, and domain restrictions are outside the parser-free contract.
- Use exact algebra or a symbolic system when coefficients are intended to be exact fractions or radicals.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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