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Multiplying Polynomials Calculator

Multiply polynomial expressions of any degree

First Polynomial

Use format: x^2 + 3x + 2 or 2x^3 - 5x + 1

Second Polynomial

Use ^ for exponents (x^2, x^3, etc.)

Distributive Property

Multiply each term by every term

a(b + c) = ab + ac

Exponent Rule

Add exponents when multiplying

x^a × x^b = x^(a+b)

Coefficient Rule

Multiply coefficients together

2x × 3x = 6x²

Combine Like Terms

Add coefficients of same power

2x² + 3x² = 5x²

(x + 2)(x² + 3x + 1)

= x(x² + 3x + 1) + 2(x² + 3x + 1)

= x³ + 3x² + x + 2x² + 6x + 2

= x³ + 5x² + 7x + 2

(2x - 1)(x² + x - 3)

= 2x(x² + x - 3) - 1(x² + x - 3)

= 2x³ + 2x² - 6x - x² - x + 3

= 2x³ + x² - 7x + 3

Algebra

• Expression expansion

• Equation solving

• Simplification

Calculus

• Derivatives

• Integration

• Taylor series

Engineering

• Signal processing

• Control systems

• Transfer functions