Multiply two polynomials up to degree 4 with step-by-step distribution, product expansion, and coefficient analysis. See the full FOIL and distribution grid.
Multiplying polynomials is a fundamental skill in algebra that extends the distributive property to expressions with multiple terms. Whether you are expanding binomials using the FOIL method or multiplying higher-degree polynomials term by term, this calculator handles it all. Enter the coefficients of two polynomials — each up to degree 4 — and instantly see the fully expanded product, the resulting degree, and the leading coefficient. The step-by-step distribution grid shows every partial product so you can follow exactly how each term in the first polynomial multiplies each term in the second. This is invaluable for homework, test prep, and verifying your own hand calculations. The calculator also highlights like terms before combining them, making it easy to see where simplification occurs. Use the built-in presets to explore classic patterns like difference of squares, perfect-square trinomials, and cube expansions without typing a single coefficient. Check the example with realistic values before reporting.
Multiplying Polynomials Calculator helps you solve multiplying polynomials problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter your inputs once and immediately inspect Polynomial A, Polynomial B, Product A·B to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
If A(x) = Σ aᵢxⁱ and B(x) = Σ bⱼxʲ, then A(x)·B(x) = Σₖ (Σᵢ₊ⱼ₌ₖ aᵢbⱼ) xᵏ. The degree of the product equals deg(A) + deg(B).
Result: Polynomial A shown by the calculator
Using the preset "Degree 0 (constant)", the calculator evaluates the multiplying polynomials setup, applies the selected algebra rules, and reports Polynomial A with supporting checks so you can verify each transformation.
This calculator takes the problem inputs and applies the relevant multiplying polynomials relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use Polynomial A, Polynomial B, Product A·B, Product Degree to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
FOIL stands for First, Outer, Inner, Last — a mnemonic for multiplying two binomials. It is a special case of the distributive property.
Yes. This calculator supports any combination of degrees from 0 to 4 for each factor.
Add the degrees of the two factors. For example, a degree-3 polynomial times a degree-2 polynomial gives a degree-5 product.
Enter 0 for any missing power. The calculator will still produce the correct product.
Yes. Multiplying polynomials and expanding brackets are two names for the same algebraic operation.
Substitute any convenient value of x into both the original factors and the product. If the numerical results match, the expansion is correct.