What is CSEEL and what does it offer?

CSEEL (Center for Scientific Exploration and Experiential Learning) is a premier Indian STEM educational initiative offering hands-on science experiments, 3D live laboratory simulations, curriculum-aligned project kits, teacher training workshops, and national science conclaves aligned with NEP 2020.

How does CSEEL support NEP 2020 experiential learning?

CSEEL shifts education from rote memorization to active inquiry and hands-on experimentation. Students observe, build, analyze, and apply scientific concepts to real-world challenges, developing critical thinking and scientific temper as envisioned by NEP 2020.

What subjects and classes are covered in CSEEL simulations and experiments?

CSEEL provides comprehensive physics, chemistry, biology, environmental science, and applied robotics experiments and virtual simulations for students from Class 6 through Class 12, mapped to CBSE, ICSE, and state curricula.

How can schools, educators, and students access CSEEL programs?

Institutions, teachers, and students can explore live simulations, order DIY lab kits, register for national seminars, and join the CSEEL EduNetwork by visiting https://www.cseel.org.

Algebraic Identity (a + b)³ 3D Dissection Model

Experiment video

What you will learn

Verify the algebraic identity (a + b)³ = a³ + 3a²b + 3ab² + b³ geometrically using a set of 8 physical 3D volumetric acrylic blocks of dimensions a and b.

Materials needed

3D Acrylic / Wooden mathematical model set for binomial cube: a = 4 cm, b = 2 cm set
3D Acrylic / Wooden mathematical model set for binomial cube: a = 4 cm, b = 2 cm set
₹50
What is it?
Montessori / CBSE standard 8-piece wooden Binomial Cube apparatus in hinged wooden box.
Specifications
Material
Fine grain seasoned beechwood
Dimensions
a = 50 mm, b = 20 mm; assembled cube = 70 mm × 70 mm × 70 mm
Color Coding
Red (a³), Black with yellow edge (3a²b), Black with blue edge (3ab²), Blue (b³)
Box
Hinged wooden storage box with printed lid diagram
- Cube of side a (4 = 64 cm³) × 1
- Cube of side a (4 = 64 cm³) × 1
₹95
What is it?
Digital Vernier Caliper for verifying block face dimensions.
Specifications
Resolution
0.01 mm
Accuracy
± 0.02 mm
- Cube of side b (2 = 8 cm³) × 1
- Cube of side b (2 = 8 cm³) × 1
₹140
What is it?
Standard laboratory apparatus used in Algebraic Identity (a + b)³ 3D Dissection Model.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard
- Cuboids of dimension a × a × b (4 = 32 cm³) × 3
- Cuboids of dimension a × a × b (4 = 32 cm³) × 3
₹185
What is it?
Standard laboratory apparatus used in Algebraic Identity (a + b)³ 3D Dissection Model.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard
- Cuboids of dimension a × b × b (4 = 16 cm³) × 3
- Cuboids of dimension a × b × b (4 = 16 cm³) × 3
₹230
What is it?
Standard laboratory apparatus used in Algebraic Identity (a + b)³ 3D Dissection Model.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard
Display tray with base 6 cm cm
Display tray with base 6 cm cm
₹275
What is it?
Standard laboratory apparatus used in Algebraic Identity (a + b)³ 3D Dissection Model.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard
Metric Vernier Caliper / Ruler
Metric Vernier Caliper / Ruler
₹320
What is it?
Standard laboratory apparatus used in Algebraic Identity (a + b)³ 3D Dissection Model.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard

Tick items as you collect them. Tap + to see the product, specifications and buy options.

Stay safe

Handle precision acrylic blocks carefully to avoid chipping corners and edges.
Ensure all 8 blocks fit together flush without gaps when building the main cube.
Label dimensions a and b clearly on each block face to facilitate spatial tracking.
Store blocks in labeled compartments to prevent losing components.

Steps

0 of 7 steps done

1Measure dimensions of each block using a ruler: confirm a = 4 cm and b = 2 cm.
Observation
Unpack the 8 polished wooden sub-blocks of the binomial cube kit; identify distinct dimensions a = 5 cm and b = 2 cm.
Safety
Inspect wooden blocks for smooth polished corners without splinters.
2Assemble all 8 blocks together inside the tray to form a large single solid cube.
Observation
Measure Block A (cube of side a = 5 cm); compute volume V = a³ = 5³ = 125 cm³.
Safety
Verify dimensions with Vernier caliper or metric ruler.
3Measure the edge of the large assembled cube: edge = a + b = 4 + 2 = 6 cm.
Observation
Identify the 3 identical square prisms of base a × a (5×5 cm) and height b (2 cm); combined volume = 3a²b = 3 × 50 = 150 cm³.
Safety
Group blocks into matching sets by shape and color.
4Calculate total volume of assembled cube: V = (a + b)³ = 6³ = 216 cm³.
Observation
Identify the 3 identical square prisms of base b × b (2×2 cm) and height a (5 cm); combined volume = 3ab² = 3 × 20 = 60 cm³.
Safety
Check that cross-sections align flush.
5Disassemble the cube and separate into 4 component categories:
Observation
Measure Block D (small cube of side b = 2 cm); compute volume V = b³ = 2³ = 8 cm³.
Safety
Ensure all 8 components are accounted for.
61 cube of a³ (volume = 64 cm³), 3 cuboids of a²b (volume = 3 × 32 = 96 cm³), 3 cuboids of ab² (volume = 3 × 16 = 48 cm³), 1 cube of b³ (volume = 8 cm³).
Observation
Assemble all 8 blocks inside the 7 cm cubic wooden box; they pack seamlessly into a single solid cube of side (a+b) = 7 cm (volume 343 cm³).
Safety
Close box lid to verify perfect flush fit without rattling or protruding.
7Sum the volumes of all 8 components: 64 + 96 + 48 + 8 = 216 cm³. Confirm (a + b)³ = a³ + 3a²b + 3ab² + b³.

Tap + on a step to see what you will observe and any safety tips.

Record your observations

Component Block Identity	Quantity in Set	Algebraic Dimensions	Volume per Block (cm³)	Total Sub-Volume (cm³)
Block A (Large Cube)	1 block	a × a × a (5 cm × 5 cm × 5 cm)	a³ = 125.0 cm³	125.0 cm³
Block B (Square Prism A)	3 blocks	a × a × b (5 cm × 5 cm × 2 cm)	a²b = 50.0 cm³	3 × 50.0 = 150.0 cm³
Block C (Square Prism B)	3 blocks	a × b × b (5 cm × 2 cm × 2 cm)	ab² = 20.0 cm³	3 × 20.0 = 60.0 cm³
Block D (Small Cube)	1 block	b × b × b (2 cm × 2 cm × 2 cm)	b³ = 8.0 cm³	8.0 cm³
Total Composite Cube	8 blocks total	(a + b)³ = (5 + 2)³ = 7³ cm³	(a + b)³ = 343.0 cm³	125 + 150 + 60 + 8 = 343.0 cm³ (Exact match)

Tap a highlighted cell to write your own observation.

Result and conclusion

An assembled cube of side (a + b) decomposes into exactly 8 geometric solid pieces: 1 cube of a³, 3 cuboids of a²b, 3 cuboids of ab², and 1 cube of b³, verifying the identity.

(a + b)³ = a³ + 3a²b + 3ab² + b³ (Volume of Large Cube = Sum of Volumes of 8 Dissected Sub-Blocks)

Observation	What it means
Exact Spatial Volume Conservation	Sum of volumes of the 8 sub-blocks (125 + 150 + 60 + 8 = 343 cm³) exactly equals volume of assembled cube (7³ = 343 cm³).
Algebraic Binomial Expansion Verified	Physical assembly provides an unforgettable three-dimensional tactile proof of (a + b)³ = a³ + 3a²b + 3ab² + b³.
Geometric Significance of Coefficients	The binomial coefficients 1, 3, 3, 1 directly represent the physical count of each distinct block shape in the expansion.
Extension to Polynomials	Generalizes spatial thinking from 2D area expansion (a + b)² = a² + 2ab + b² to three-dimensional Euclidean volumes.

Volume Breakdown of the 8 Sub-Blocks Comprising (a + b)³

Sample readings. Replace with your own results.

Experiment photos

Before the experimentDuring the experimentResult