Discussion
The expression 9x2 - 12xy + 21x + 4y2 - 14y + 12 is factorised as :
Answer: A
The factorisation is (3x - 2y + 3)(3x - 2y + 4).
Group the terms around \(t = 3x - 2y\):
\[ \begin{aligned} 9x^{2} - 12xy + 4y^{2} &= (3x - 2y)^{2} = t^{2} \\ 21x - 14y &= 7(3x - 2y) = 7t \end{aligned} \]
So the expression is a quadratic in \(t\):
\[ \begin{aligned} t^{2} + 7t + 12 &= (t + 3)(t + 4) \\ &= (3x - 2y + 3)(3x - 2y + 4) \end{aligned} \]
Options with \(3x + 2y\) would give \(+12xy\) and \(+14y\), the wrong signs. (t + 2)(t + 6) multiplies out to \(t^{2} + 8t + 12\), not \(t^{2} + 7t + 12\).
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