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  1. Glossary
  2. /Mathematics
  3. /Algebraic Identity

What is Algebraic Identity?

In short

An algebraic identity is an equation that is true for every value of the variables, such as (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2.

In simple words

An equation is true only for certain values. An identity is true for all. The standard identities are (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2, (a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2(a−b)2=a2−2ab+b2 and a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b). For cubes, a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a+b)(a^2 - ab + b^2)a3+b3=(a+b)(a2−ab+b2). They are used to expand, to factorise and to do mental arithmetic.

Example

8x3−27y3=(2x)3−(3y)3=(2x−3y)(4x2+6xy+9y2)8x^3 - 27y^3 = (2x)^3 - (3y)^3 = (2x - 3y)(4x^2 + 6xy + 9y^2)8x3−27y3=(2x)3−(3y)3=(2x−3y)(4x2+6xy+9y2), using a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2)a3−b3=(a−b)(a2+ab+b2).

Also searched as: 8x 3 27y 3, product of two sums.

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Related terms

  • Polynomial
  • Quadratic Equation

← All glossary terms

Learn it in

  1. Factorising Polynomials and IdentitiesClass 9 to 10
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Practise

  1. Let x, y and z be real numbers with x, y, z ≥ 0 and x + y + z = 6, and put E = x²y + y²z…Advanced
  2. Show that if x + y + z = 0, then x³ + y³ + z³ = 3xyz. Use it to find 9³ + (-4)³ + (-5)³.Hard
  3. Factorise 27x³ + 64y³.Medium
  4. Expand (3x + 2y)² and (x - 3y)³.
Medium
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Quick questions

  1. Factorise x³ + 27.Medium
  2. A square of side a + b is cut into four parts. Which drawing labels the areas of the…Medium
  3. a + b = 7 and ab = 10. What is a² + b²?Medium

More Mathematics terms

  1. Arithmetic Progression
  2. Complex Number
  3. Derivative
  4. Function
  5. Isosceles Triangle
  6. Linear Equation
All Mathematics terms →

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