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Factorise the following expressions: x2 - 9, x2 - 64, 9y2 - 81

Mathematics

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Your solutions for all three factorization problems are correct! You have correctly applied the difference of two squares formula.

Here's a breakdown of the method for the first problem as an example:

The general formula for the difference of two squares is:

a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b)
  • : Factorise x2−9x^2 - 9

  1. Identify a2a^2 and b2b^2.

    Here, $a^2 = x^2$, so $a = x$.  
And $b^2 = 9$, so $b = \sqrt{9} = 3$.

  2. Apply the difference of two squares formula.

    $$
x^2 - 9 = (x-3)(x+3)
$$
Your answer: $\boxed{(x-3)(x+3)}$

    • : Factorise x2−64x^2 - 64 Here, a=xa = x and b=64=8b = \sqrt{64} = 8.

      x2−64=(x−8)(x+8)x^2 - 64 = (x-8)(x+8)

      Your answer: (x−8)(x+8)\boxed{(x-8)(x+8)}

    • : Factorise 9y2−819y^2 - 81 Here, a=9y2=3ya = \sqrt{9y^2} = 3y and b=81=9b = \sqrt{81} = 9.

      9y2−81=(3y−9)(3y+9)9y^2 - 81 = (3y-9)(3y+9)

      Your answer: (3y−9)(3y+9)\boxed{(3y-9)(3y+9)}

    All your answers are correct!

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