Mathematics
Consider the following two statements.
Statement 1: The factorisation of x2 + 2x + 1 is (x - 1)2.
Statement 2: (a - b)2 = a2 + 2ab + b2.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Factorisation
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Answer
Given,
⇒ x2 + 2x + 1
⇒ x2 + 2.x.1 + 12
⇒ (x + 1)2
∴ Statement 1 is false.
⇒ (a - b)2
⇒ (a - b)(a - b)
⇒ a(a - b) - b(a - b)
⇒ a2 - ab - ab + b2
⇒ a2 - 2ab + b2
∴ Statement 2 is false.
∴ Both statements are false.
Hence, option 2 is the correct option.
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