Cubes of Algebra for School Maths Lab

Quick Answer: Cubes of Algebra for School Maths Lab is a set of solid pieces that fit together into cubes, used to model algebraic identities for cubes as volumes. Students assemble the cubes of algebra pieces and compare the volume of each part with the terms of the expansion.

Moving From Area to Volume Identities

Students usually meet identities first as areas, with (a + b)² drawn as a square. Identities for cubes are the next step, and they are hard to picture on paper because the pieces are three-dimensional. Solid pieces solve that problem: a cube of edge a + b, taken apart, shows that its volume is made up of smaller cubes and cuboids whose volumes can each be written in terms of a and b.

A numerical lesson makes this concrete. If a stands for 3 cm and b for 2 cm, the whole cube has edge 5 cm and volume 125 cm³. For the cube of a sum, the pieces then have volumes of 27 cm³ for a³, 8 cm³ for b³, and 18 cm³ and 12 cm³ for the cuboids a²b and ab², three of each. Adding 27 + 54 + 36 + 8 gives 125, so students see (a + b)³ = a³ + 3a²b + 3ab² + b³ hold before they prove it by multiplication.

The listing does not state which cube identities this set covers. Sets of this kind are used for the cube of a sum, and some also model the cube of a difference or the sum and difference of two cubes, so confirm the identities included, the number of pieces and the material before ordering. For a set named specifically for (a + b)³, see the Cubic Identities (a+b)3 model.

Applications

• Showing a cubic identity as the volume of a cube built from smaller solids
• Checking an identity numerically by giving a and b lengths
• Linking the area identities for squares with the volume identities for cubes
• Building and dismantling the cube in groups before the algebraic proof

Specifications

Care & Handling

• Keep all pieces of one cube together; each piece is needed for the whole to fit.
• Store pieces in their box rather than loose, so edges and corners are not chipped.
• Wipe with a dry or slightly damp cloth and dry before packing away.

Why Choose LabEquip

Class 9 and 10 maths teachers buy solid identity sets when algebra moves from squares to cubes. LabEquip lists this set in its Mathematics School Lab Products range; send the identities you need to teach through the contact page.

Frequently Asked Questions

How do solid pieces show the identity for (a + b)³?

A cube of edge a + b is split by cuts at distance a along each edge. That gives one a-by-a-by-a cube, one b-by-b-by-b cube, three cuboids measuring a by a by b and three measuring a by b by b, which match a³, b³, 3a²b and 3ab².

Why are three-dimensional models needed for cube identities?

A cube identity describes a volume, and a flat drawing hides some of the pieces behind others. Holding and separating the solids lets students count every part, which is where most errors with the middle terms come from.

How can the identity be checked with numbers?

Choose lengths for a and b, work out the volume of each piece, and add them. With a = 3 and b = 2, the parts come to 27 + 54 + 36 + 8, which equals 125, or 5³.

What is the difference between this set and the Cubic Identities (a+b)3 model?

The Cubic Identities model is named for the single identity (a + b)³, while this listing is more general in name. Both rest on the same volume principle, so check which cube identities this set covers when you enquire.

How is a³ − b³ shown with solids?

Where a set includes pieces for it, a³ − b³ is shown by removing a small cube of edge b from a corner of a cube of edge a and splitting the remaining solid into three cuboids whose total volume is (a − b)(a² + ab + b²).

At what level are cube identities taught?

In NCERT-based schools, identities for (x + y)³ and (x − y)³ appear in the Class 9 chapter on polynomials, and they are used again in factorisation problems in later classes.

Last Updated: September 2026