FOIL plus general distribution.
Two binomials get the classic FOIL treatment. Anything longer uses the same logic generalized, with each term-pair multiplication shown in sequence.
Two methods
AI Solver by AskSia
Multiplying Polynomials Solver: every pairing shown
Whether it is two binomials, a binomial times a trinomial, or three polynomials in a row, AskSia distributes every term and shows every multiplication. Coefficients multiply, exponents add, signs follow standard rules, and like terms combine into a clean standard-form polynomial.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you multiply polynomials?
To multiply polynomials, distribute each term of the first polynomial across every term of the second. For two binomials this is the FOIL pattern (First, Outer, Inner, Last). For longer polynomials, generalize: every term on the left pairs with every term on the right. Multiply coefficients, add exponents of like bases, track signs, then combine like terms by degree. Write the answer in descending-degree standard form.
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problems solved
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avg solve time
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study-ready explanations
Why AskSia Solver
How AskSia handles polynomial multiplication.
Built for the moments when a problem has more terms than FOIL can label.
Multi-polynomial products.
Multiply three or four polynomials together. AskSia handles them in stages, showing the intermediate polynomial after each multiplication.
Stacked
Special products spotted.
(a+b)(a-b), (a+b)^2, (a-b)^2, and cube identities get recognized and labeled, so the shortcut pattern becomes second nature.
Patterns
Standard-form output.
After combining like terms, the answer appears in descending-degree order with leading coefficient first.
Standard form
Photo of your worksheet.
Snap your homework and AskSia parses both polynomials, even with handwritten exponents.
Multi-modal
Graph for visual check.
Quadratic, cubic, and quartic expansions get plotted with roots and turning points labeled.
Visual
How It Works
Multiply polynomials in three steps.
Step 01
Enter both polynomials.
Type, paste, snap a photo, or speak the product. AskSia parses each polynomial and counts its terms.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
Watch distribution.
Every term from the first multiplies every term from the second. Each pairing shows coefficient arithmetic, exponent addition, and sign tracking.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the simplified polynomial.
Like terms group by degree, sum, and produce a standard-form answer. A graph appears when degree allows visualization.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
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Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
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Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
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1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What multiplying polynomials covers.
Standard FOIL practice.
(x+3)(x-7), (2x-1)(x+4), and the rest of Algebra 1 binomial work. Every pairing labeled.
Algebra 1
Binomial times trinomial.
(x+2)(x^2-3x+5) and similar Algebra 2 problems. Six term-pairs, all shown.
Algebra 2
Three or more polynomials.
Multiply (x+1)(x-2)(x+3) by chaining. AskSia shows each intermediate result.
Chained
Pre-calculus expansion.
Binomials raised to powers, polynomials with complex coefficients, and expansions used in partial fractions.
Pre-Calc
Verify factored form.
Given a factored polynomial, expand to check that you can recover the original standard form.
Check
SAT, ACT, AP Algebra.
Polynomial multiplication shows up across standardized tests. AskSia handles every common pattern with the steps you need to learn.
Test prep
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
What is the difference between FOIL and distribution?
FOIL is just distribution for the special case of two binomials, with a memorable name for each of the four products. Distribution is the general rule that applies to polynomials of any length. AskSia uses FOIL labels when both factors are binomials and switches to general distribution for longer polynomials, with the underlying logic identical.
Can I multiply polynomials with multiple variables?
Yes. AskSia handles polynomials in x and y, or any letter set. Each variable's exponents are tracked independently when multiplying terms, and the final answer is organized in a sensible order (typically descending in the primary variable).
Will it expand something like (a+b+c)^2?
Yes. AskSia treats (a+b+c)^2 as (a+b+c)(a+b+c), distributes all nine term-pairs, and combines like terms to give a^2 + b^2 + c^2 + 2ab + 2bc + 2ac. The expansion identity is also stated as a pattern you can reuse.
How are like terms identified?
Two terms are like terms when they have the exact same variable parts with the exact same exponents, regardless of coefficient. AskSia groups them by these variable signatures and shows the coefficient addition, so 3x^2 + 5x^2 becomes 8x^2 with the grouping made visible.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Every term, every pairing, every step.
Join 2M+ students using AskSia to multiply polynomials with full transparency. FOIL, distribution, special products, photo input, and a graph on every result.
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