AI Diamond Problem Solver

Product on top, sum on bottom. Find the two numbers.

AskSia solves any diamond problem step-by-step. Given the product (top of the diamond) and the sum (bottom), AskSia lists every factor pair, identifies the pair that matches both, and shows how the result connects to factoring a quadratic ax² + bx + c.

Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
Quick Answer

What is the AskSia diamond problem solver?

The AskSia diamond problem solver is an AI tool for Algebra 1 and Algebra 2 students that finds two numbers given their product and sum (the diamond problem setup). AskSia lists every factor pair of the product, identifies the pair whose sum matches, and shows the diamond diagram with both numbers placed correctly. The same method connects directly to factoring quadratic trinomials ax² + bx + c, so the diamond problem isn't just a puzzle, it's the engine behind quadratic factoring.

98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver

Diamond problems and factoring, finally clicking together.

The diamond problem isn't an isolated puzzle. AskSia connects it directly to factoring quadratics, so once you can solve the diamond, you can factor the trinomial.

Lists every factor pair

Given the product, AskSia lists all integer factor pairs (positive and negative). For a product of 12, that's (1,12), (2,6), (3,4), (negative 1, negative 12), and so on. The full list is shown so you can verify nothing is missed.

Every pair listed

Identifies the pair that sums correctly

From the factor pair list, AskSia picks the pair whose sum matches the bottom of the diamond. The check is shown: the product is verified, then the sum is verified, so both diamond conditions are met.

Sum and product both checked

Handles negative products and sums

When the product is negative, one factor must be negative and the other positive. AskSia explains the sign rules clearly: same signs gives positive product, opposite signs gives negative product. The work is fully shown for negative cases.

Sign rules explained

Connects to factoring quadratics

Once you find the diamond solution for ac product and b sum, you can factor the trinomial x² + bx + c as (x + p)(x + q) where p and q are the diamond numbers. AskSia makes this connection explicit on every solve.

Factoring bridge

AC method for harder trinomials

For trinomials ax² + bx + c with a ≠ 1, the diamond gets the ac product and b sum. AskSia explains the AC method extension and walks through the grouping step that follows.

AC method

Diamond diagram drawn

Every solve includes the diamond diagram with the product (top), sum (bottom), and the two numbers (left and right). Useful for homework that asks you to draw the diamond as part of the answer.

Diagram included
How It Works

Three taps to a solved diamond.

Step 01

Capture the diamond

Snap a photo of the diamond from your textbook, paste the product and sum, or type them into the built-in calculator. AskSia identifies the two known values.

Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02

Watch Sia list factor pairs

AskSia lists every integer factor pair of the product systematically, then checks each pair's sum against the diamond bottom. The matching pair is identified within seconds.

Calculus · Step 4 of 4
1.4s
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

See the diamond completed

The two numbers are placed in the left and right of the diamond, and the connection to factoring quadratics is shown alongside. Useful for the immediate next problem on your worksheet.

Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On

Solve anywhere
you study.

Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.

Web App

Full study studio

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
app.asksia.ai/solver
Hi! What are we studying today?
Ask about your homework, lecture, or readings...
Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App

Snap & solve, anywhere

Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.

One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
AskSia
+
What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases

Every diamond problem use case.

📐

Algebra 1 introduction

First-time diamond problems with small positive integers. AskSia explains the diamond layout, lists factor pairs, and finds the matching pair in clear, step-by-step language.

Algebra 1 intro
⚛️

Factoring quadratics x² + bx + c

Diamond problems are the engine behind factoring x² + bx + c. AskSia shows how the diamond solution gives the two binomials directly: (x + p)(x + q).

Quadratic factoring
🧪

AC method for ax² + bx + c

When the leading coefficient is not 1, the diamond uses the AC product and b sum. AskSia walks through the AC method extension and the grouping step that follows.

AC method
🧬

Negative products and sums

Diamond problems with negative numbers require careful sign analysis. AskSia explains which factor must be negative and walks through the candidate pairs systematically.

Negative cases
💻

CPM and integrated math curricula

Many CPM and integrated math programs use the diamond problem as a core tool. AskSia matches the curriculum's notation and shows the diamond diagram explicitly.

CPM, integrated
🎯

Quick practice and drills

After any diamond solve, generate similar problems at the same difficulty for quick practice. Build a flashcard set on factor pairs for review.

Practice drills
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 comparison between AskSia Solver and alternatives
FeatureAskSia SolverChatGPTPhoto Solvers
Solution accuracy✓ 98%~70-85%, hallucinations~90%, math only
Auto-generated diagrams✓ Every solveInconsistent / brokenGraphs only, math-only
Step-by-step explanations✓ Numbered + plain EnglishInconsistent depth✓ Math steps
Subject coverage✓ Math, Physics, Chem, Bio, CS, Econ✓ Wide but unverifiedMath only
Photo input✓ Handwriting + diagrams + codePhotos OK, weak on handwriting✓ Math photos only
Answer verification✓ Self-checked before displayNo verificationMath engine only
Tutor follow-ups✓ Hints, alt methods, ELI5✓ General chatNot available
Practice and flashcards✓ One-tap from any solveManual promptingNot available
Code debugging✓ Python, Java, C++, SQL...✓ YesNot available
Free to start✓ Daily solves, no cardLimited model accessSteps locked behind paywall
FAQ

Frequently asked questions.

What is a diamond problem in math?
A diamond problem is a visual layout used in Algebra 1 and Algebra 2 (especially in CPM and integrated math curricula) to find two numbers given their product and sum. The diamond has four sections: top (product), bottom (sum), left and right (the two numbers to find). The goal is to fill in the left and right so that left × right equals the top and left + right equals the bottom. The diamond is the engine behind factoring quadratic trinomials of the form x² + bx + c.
How does AskSia solve a diamond problem?
AskSia lists every integer factor pair of the product (top of the diamond), then checks each pair's sum against the bottom of the diamond. The pair whose sum matches is the answer, and gets placed in the left and right of the diamond. For negative products, AskSia uses sign rules: same signs give a positive product, opposite signs give a negative product. The full factor pair list is shown so you can see the method, not just the answer.
How is the diamond problem connected to factoring quadratics?
The diamond problem is literally the setup for factoring quadratic trinomials x² + bx + c. The product (top of the diamond) is c, the sum (bottom) is b, and the two numbers found (left and right) become the constants in the factored form (x + p)(x + q). So once you can solve the diamond, you can factor the trinomial. AskSia shows this connection on every solve and writes out the factored form directly.
What if the leading coefficient is not 1, like 2x² + 7x + 3?
For trinomials ax² + bx + c with a ≠ 1, the diamond is modified: the top of the diamond becomes the product ac (not just c), and the bottom is still b. The two numbers found are then used in the AC method: split the middle term, group, and factor. AskSia walks through the AC method extension explicitly when a ≠ 1, so the diamond and the grouping step connect cleanly.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. 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.
Start Today

Diamond solved. Trinomial factored.

Join 2M+ students using AskSia to solve diamond problems and factor quadratic trinomials with the factor pair method, sign rules, and the AC method extension shown on every solve.

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