Question 35

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waecmaths question: 

Find the coefficient of m in the expansion of $\left( \frac{m}{2}-1\frac{1}{2} \right)\left( m+\frac{2}{3} \right)$

Option A: 

$-\frac{1}{6}$

Option B: 

$-\frac{1}{2}$

Option C: 

–1

Option D: 

$-1\tfrac{1}{6}$

waecmaths solution: 

$\begin{align}  & \left( \frac{m}{2}-1\frac{1}{2} \right)\left( m+\frac{2}{3} \right)=\left( \frac{m}{2}-\frac{3}{2} \right)\left( m+\frac{2}{3} \right) \\ & =\frac{{{m}^{2}}}{2}+\frac{2m}{6}-\frac{3m}{2}-\frac{6}{6} \\ & =\frac{{{m}^{2}}}{2}+\frac{m}{3}-\frac{3m}{2}-1 \\ & =\frac{{{m}^{2}}}{2}+\left( \frac{2m-9m}{6} \right)-1 \\ & =\frac{{{m}^{2}}}{2}-\frac{7m}{6}-1 \end{align}$The coefficient of m is $-\frac{7}{6}=-1\frac{1}{6}$

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