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Common mistakes made when working on algebraic identities

Though the students enjoy working on algebraic identities, however in many cases they tend to make mistakes. These mistakes could be because of carelessness or because the child did not understand the concept properly. It is always a good idea to be aware about the common mistakes which students usually make so that these can be corrected from the early age. Here are some of the common mistakes which students usually make when working on algebraic identities.

☞ (a+b)²=a²+b²

The correct answer is (a+b)²=a²+2ab+b²

Ways to teach the children to minimize this error
  • (a+b)²
    =(a+b)(a+b)
    =a×a+a×b+b×a+b×b
    =a²+2ab+b²
  • ☞ (a−b)²=a²−b²

    The correct answer is (a−b)²=a²−2ab+b²

    Ways to teach the children to minimize this error
  • (a−b)²
    =(a−b)(a−b)
    =a×a−a×b−b×a+b×b
    =a²−2ab+b²
  • ☞ (a−b)²=a²+2ab−b²

    The correct answer is (a+b)²=a²−2ab+b².

    Ways to teach the children to minimize this error
  • (a−b)².
    =(a−b)(a−b)
    =a×a−a×b−b×a+b×b
    =a²−2ab+b²
  • ☞ (a−b)³=a³−b³

    (a−b)³=a³−3a²b+3ab²−b³ (≠ a³−b³)

    Ways to teach the children to minimize this error
  • (a−b)³
    =(a−b)(a−b)(a−b)
    =(a−b)(a²−2ab+b²)
    =a³−3a²b+3ab²−b³
  • ☞ (a+b)³=a³+b³

    (a+b)³=a³+3a²b+3ab²+b³ (≠ a³+b³)

    Ways to teach the children to minimize this error
  • (a+b)³
    =(a+b)(a+b)(a+b)
    =(a+b)(a²+2ab+b²)
    =a³+3a²b+3ab²+b³
  • ☞ (a+b+c)²=a²+b²+c²

    (a+b+c)²=a²+b²+c²+2ab+2bc+2ca (≠ a²+b²+c²)

    Ways to teach the children to minimize this error
  • (a+b+c)²
    =(a+b+c)(a+b+c)
    =a²+b²+c²+2ab+2bc+2ca


  • The best way to remove the above confusion and to ensure the children have less chance of committing mistakes is to practice the problems related to the above situations. Click on Algebraic Identities to practice.



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    Given below are other commonly made mistakes in Math:
    Clock Reading Time | Exponents & Power | Whole to number-word | Square root | Lines & Angles | Integers | Area Plane Figure | Perimeter Plane Figure | Algebraic Identities | Congruence of Triangles | Similar Triangles | Coordinate Geometry | Trigonometry | Solving equations | Polynomial | Division | Algebraic Expression | Average |
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