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NSW Y8 Maths Algebra Factorising with Negatives

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Factorising with Negatives Theory

The highest common factor \((HCF)\) of \(-4 x^2 y\) and \(2 x\) is \(-2 x\) or \(2 x\).\\ \(\begin{aligned} \text{Since } -4 x^2 y&=-2 x \times 2 x y \text{ and } 2x=-2 x \times -1\\ \text{ or } -4x^2y&=2 x \times-2 x y \text{ and } 2 x=2 x \times 1 \end{aligned}\)\\ \begin{multicols}{2} \textbf{Example 1}\\ Factorise \(-4 x^2 y+2 x\) with a negative included in the HCF.\\ \textbf{Example 1 solution}\\ \(\begin{aligned} -4 x^2 y+2 x & =-2 x \times 2 x y+-2 x \times -1 \\ & =-2 x(2 x y-1). \end{aligned}\) \columnbreak \textbf{Example 2}\\ Factorise \(3 x y^2 z-a x y z\) with a negative included in the HCF\\ \textbf{Example 2 solution}\\ \(\begin{aligned} 3 x y^2 z-9 x y z & =-3 x y z \times -y+-3 x y z \times 3 \\ & =-3 x y z(-y+3) \\ & =-3 x y z(3-y) \end{aligned}\) \end{multicols}

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Videos

Videos relating to Factorising with Negatives.

  • Factorising with Negatives - Video - Factorising Expressions - Example 1

  • Factorising with Negatives - Video - Factorising Expressions - Example 2

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