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Two-Binomial Product & Coefficient Working
Expand (a₁x + a₀)(b₁x + b₀) into quadratic, linear and constant coefficients, including the two cross-products.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Multiplying (2x + 3)(4x − 5) gives 8x² + 2x − 15.
c₂ = a₁b₁; c₁ = a₁b₀ + a₀b₁; c₀ = a₀b₀
Worked example
Enter these known values and leave the other values blank.
- First factor: coefficient of x (a₁)
- 2
- First factor: constant (a₀)
- 3
- Second factor: coefficient of x (b₁)
- 4
- Second factor: constant (b₀)
- -5
- Product: coefficient of x²
- 8
- Product: coefficient of x
- 2
- Product: constant
- -15
Assumptions and limitations
- Enter real numeric coefficients. Negative and zero coefficients are valid; zero leading coefficients can reduce the degree of the product.
- All terms use the same symbolic variable x. The tool computes coefficients, not roots of the resulting polynomial.
- Available reverse equations require sufficient known nonzero factors; they do not provide a unique general factorization of an arbitrary quadratic.
Common questions
Why are there two cross-products?
The x term receives a₁x multiplied by b₀ and a₀ multiplied by b₁x. Their coefficients add to c₁.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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