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Algebra

Question 2 of 9

Factorising Quadratic Equations

Question

Factorise \(9y^2 - 4 = 0\)

Show solution Hide solution Fully worked — 3 steps
  1. Factorise
    \[ 9y^2 - 4 = 0 \]
    \[ (3y - 2)(3y + 2) = 0 \]
  2. Using the zero-factor theorem, equate each factor to 0

    Then either

    \[ 3y - 2 = 0 \Rightarrow y = \frac{2}{3} \]

    or

    \[ 3y + 2 = 0 \Rightarrow y = \frac{-2}{3} \]
  3. State the solutions

    The solutions are \(y = \frac{2}{3}\) or \(y = \frac{-2}{3}\). That is, \(y\) is two thirds and \(y\) is minus two thirds.