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Factorise. x2−2x+1=0x^2 - 2x + 1 = 0

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Q. Factorise. x2−2x+1=0x^2 - 2x + 1 = 0
  1. Recognize Equation Form: Recognize the quadratic equation and identify its standard form. A quadratic equation is in the form ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=−2b = -2, and c=1c = 1.
  2. Identify Perfect Square Trinomial: Look for a perfect square trinomial. The given quadratic equation x2−2x+1x^2 - 2x + 1 resembles the square of a binomial because it follows the pattern a2−2ab+b2a^2 - 2ab + b^2, which factors into (a−b)2(a - b)^2.
  3. Factor Using Binomial Pattern: Factor the quadratic equation using the square of a binomial pattern.\newlineThe factors of x2−2x+1x^2 - 2x + 1 are (x−1)(x−1)(x - 1)(x - 1) or (x−1)2(x - 1)^2, since (x−1)2=x2−2x+1(x - 1)^2 = x^2 - 2x + 1.

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