Expand Polynomials Calculator
Multiply and expand polynomial expressions using FOIL, binomial theorem, and general expansion with detailed steps.
How to Expand Polynomials
Polynomial expansion multiplies factors to produce a simplified sum of terms. Common techniques include FOIL for binomial products, the binomial theorem for powers, and the distributive property for general expressions.
FOIL Method
For $(ax+b)(cx+d)$, FOIL means First, Outer, Inner, Last:
$$(ax+b)(cx+d) = acx^2 + (ad+bc)x + bd$$Binomial Theorem
$$(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$$Pascal's triangle provides binomial coefficients quickly for small powers.
Input Tips
- Use ^ for exponents:
(x+1)^3 - Implicit multiplication works:
2x - Multiply grouped factors:
(x+2)(x+3)
Related tools: try the FOIL Method Calculator and Algebraic Expression Simplifier.
Frequently Asked Questions
What is the expanded form of (x+2)(x+3)?
The product expands to $x^2 + 5x + 6$ using FOIL or distributive multiplication.
When should I use the binomial theorem?
Use it for expressions like $(a+b)^n$ where $n$ is a non-negative integer. It gives each term's coefficient directly.
Can this expand trinomial products?
Yes. Expressions such as $(x+1)(x^2+2x+3)$ are handled by distributing each term in the first factor across the second factor.
What is the difference between expanding and factoring?
Expanding turns products into sums. Factoring does the reverse by rewriting sums as products. Both are core algebra skills.
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