The binomial multiplication calculator is a tool designed to compute the product of two binomials. A binomial typically takes the form (ax ± b), where:
This calculator automatically expands expressions of the form (a₁x ± b₁)(a₂x ± b₂) and provides detailed step-by-step calculations to help users understand the process of binomial multiplication.
Enter the binomials into the two input fields of the calculator:
First binomial: Coefficient of x (e.g., 2), choose + or -, constant term (e.g., 3)
Example: 2x + 3
Second binomial: Coefficient of x (e.g., 4), choose + or -, constant term (e.g., 5)
Example: 4x - 5
Click the "Calculate" button.
The calculator will automatically expand and compute:
(2x + 3)(4x - 5) = 8x² - 10x + 12x - 15 = 8x² + 2x - 15
and display detailed calculation steps.
The calculator shows step-by-step as follows:
Original expression: (2x + 3)(4x - 5)
Expand using the FOIL method (First, Outer, Inner, Last):
First (first terms multiplied): 2x × 4x = 8x²
Outer (outer terms multiplied): 2x × (-5) = -10x
Inner (inner terms multiplied): 3 × 4x = 12x
Last (last terms multiplied): 3 × (-5) = -15
Combine like terms: 8x² - 10x + 12x - 15 = 8x² + 2x - 15