Add, subtract, and multiply polynomials. Enter two polynomials and select an operation to see step-by-step solutions.
Enter coefficients as comma-separated values (highest power to constant term)
Add coefficients of like terms (same degree):
(2x² + 3x + 1) + (x² - 2x + 4) = 3x² + x + 5
Subtract coefficients of like terms (same degree):
(2x² + 3x + 1) - (x² - 2x + 4) = x² + 5x - 3
Multiply each term of the first polynomial by each term of the second:
(x + 2)(x + 3) = x² + 5x + 6
The FOIL method for binomials:
Add: (2x² + 3x - 1) + (x + 4)
Align like terms
2x² + (3x + x) + (-1 + 4)
2x² + 4x + 3
Subtract: (x² + 5x + 6) - (x + 2)
Distribute negative sign
x² + 5x + 6 - x - 2
x² + 4x + 4
Multiply: (x + 2)(x + 3)
FOIL: x² + 3x + 2x + 6
x² + 5x + 6
Multiply: (x² + 1)(x² - 1)
Difference of squares
x⁴ - 1
Multiply: (2x + 1)(3x² - 2x + 4)
Distribute: 6x³ - 4x² + 8x + 3x² - 2x + 4
6x³ - x² + 6x + 4