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factorise " \& "x^(2)-9

factorise\newline & x2−9 \text { \& } x^{2}-9

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Full solution

Q. factorise\newline & x2−9 \text { \& } x^{2}-9
  1. Recognize Difference of Squares: Recognize that x2−9x^2 - 9 is a difference of squares.\newlinex2−9=(x)2−(3)2x^2 - 9 = (x)^2 - (3)^2
  2. Apply Formula: Apply the difference of squares formula: a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b). (x2−9)=(x+3)(x−3)(x^2 - 9) = (x + 3)(x - 3)
  3. Check Solution: Check the solution by expanding (x+3)(x−3)(x + 3)(x - 3) to ensure it equals x2−9x^2 - 9.\newline(x+3)(x−3)=x2−3x+3x−9(x + 3)(x - 3) = x^2 - 3x + 3x - 9\newline=x2−9= x^2 - 9

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