Polynomial multiplication distributes every term in one polynomial across every term in the other. Coefficients multiply, exponents add, and products with the same final power are combined into one simplified polynomial.
⚠Note: Enter coefficients in descending degree order. Missing middle terms should be entered as 0 so powers stay aligned correctly.
How Polynomial Multiplication Works
Multiply all term pairs, track the new powers, then combine coefficients that land on the same exponent.
Distributive Property
Every term in one polynomial multiplies every term in the other.
Power Addition
When x powers multiply, their exponents add.
Like Terms
Products with the same final power are added together.
Degree
The product degree is usually the sum of the input degrees.
💡 Example: (2x+3)(4x-5) gives 8x²-10x+12x-15, so the product is 8x²+2x-15.
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