Study Guides/Maths/Mathematical Identities
Study Guide · Maths

Standard Algebraic Mathematical Identities

In Mathematics, an Identity is an equation that is always true, no matter what values you plug into the variables. Memorizing standard algebraic identities is crucial for solving polynomial problems quickly.

Question (Click to Flip)

What is a mathematical identity?

Answer

A mathematical identity is an algebraic equation that remains true regardless of the values substituted for its variables.

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Key Facts

Identity: An equation that holds true for ALL values of its variables.

Most used: (a+b)(a-b) = a² - b².

Difference from Equation: An equation like 2x = 4 is only true for x=2. But (x+1)² = x²+2x+1 is an identity because it is true for any number.

The 4 Standard Identities (Class 8)

These are the foundational identities that you will use throughout your math education:

  1. Square of a sum: $(a + b)² = a² + 2ab + b²$
  2. Square of a difference: $(a - b)² = a² - 2ab + b²$
  3. Difference of squares: $(a + b)(a - b) = a² - b²$
  4. Product of binomials: $(x + a)(x + b) = x² + (a + b)x + ab$

Advanced Identities (Class 9)

As you progress, you must learn the identities involving three variables and cubes: 5. Square of a trinomial: $(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca$ 6. Cube of a sum: $(a + b)³ = a³ + b³ + 3ab(a + b)$ 7. Cube of a difference: $(a - b)³ = a³ - b³ - 3ab(a - b)$ 8. Sum/Difference of cubes:

  • $a³ + b³ = (a + b)(a² - ab + b²)$
  • $a³ - b³ = (a - b)(a² + ab + b²)$

Questions and Answers

What is a mathematical identity?+

A mathematical identity is an algebraic equation that remains true regardless of the values substituted for its variables.

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