Algebraic Identity (a + b)³

Objective

To verify the algebraic identity: (a + b)³ = a³ + b³ + 3a²b + 3ab².

Pre-requisite Knowledge

  • Concept of the cube.
  • Concept of the cuboid.
  • Addition of terms.
  • Multipication of numbers.
  • Prior knowledge of the volume of cubes/cuboids.

Concept

  • An Algebraic Identity is equality, which is true for all the values of the variables in the equality. They are also used for the factorization of polynomials. The algebraic equations which are valid for all values of variables in them are called algebraic identities.
  • In this way, algebraic identities are used in the computation of algebraic expressions and solving different polynomials.

Cube

A cube is a region of space formed by six identical square faces joined along their edges. Three edges join at each corner to form a vertex.

Volume of Cube

  • The volume of the cube is the space contained in it. Suppose, if an object is cubical and we need to immerse any material in it, say water, then the measure of water in litres to be kept in the object is calculated by its volume.
  • The formula of the volume is given by : Volume of cube = (side)³ (cubic units)

 

Cuboid

A cuboid is a 3-D shape with rectangular sides. Cuboids have six surfaces and twelve edges. Objects that are cuboid include books, match-boxes and shoe boxes. If a cuboid has faces that are all square it is a cube. All the angles of a cuboid are right angles.

Volume of Cuboid

  • The volume of a cuboid is the total spaces occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces.
  • Therefore, the volume is a measure based on the dimensions of these faces, i.e. length, width and height.
  • Volume of cuboid = length * width * height (cubic units)