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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

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