Factorise : $9 x^{2} - 12 x + 4 - 4 y^{2}$

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Solution

$9 x^{2} - 12 x + 4 - 4 y^{2}$

$= [(3 x)^{2} - 2 \times 3 x \times 2 + (2)^{2}] - 4 y^{2}$

$= (3 x - 2)^{2} - (2 y)^{2}$

$= (3 x - 2 + 2 y) (3 x - 2 - 2 y)$ $[a^{2} - b^{2} = (a + b) (a - b)]$

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