Free · Algebra and geometric relations
Binomial Products by Four Terms
Expand linear or positive-integer-power binomials and inspect the four products.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
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
For the worked example, first = 8, outer = 10, inner = 12, last = 15, sum lin = 22.
(axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd
Worked example
Enter these known values and leave the other values blank.
- Mode
- 1
- a
- 2
- b
- 3
- c
- 4
- d
- 5
- Result
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. a = 2.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. b = 3.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. c = 4.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. d = 5.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. a = 2. c = 4.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. first = 8.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. a = 2.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. d = 5. outer = 10.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. b = 3. c = 4.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. inner = 12.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. b = 3. d = 5. last = 15.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. first = 8.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. outer = 10.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. inner = 12.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. last = 15.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. a = 2.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. b = 3.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. c = 4.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. d = 5.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. first = 8.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. sum lin = 22.
- Explanation
- (axⁿ+b)(cxᵐ+d) = acxⁿ⁺ᵐ + adxⁿ + bcxᵐ + bd. last = 15.
Assumptions and limitations
- General exponents are positive integers. Equal exponents combine the middle terms; unequal exponents remain separate.
- This expands coefficients and exponents rather than evaluating x.
Common questions
How do I use this relation?
Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.
What do the displayed numbers mean?
The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
Related calculators
Explore algebra and geometric relations or browse all math calculators.