Simplify the expression $\frac{a^{2} m^{2} - 2 a m - 2 a^{3} m + (a^{2} m)^{2}}{(2 - a m)}$ and hence identify which of the following is not a factor of the simplified expression.

a m

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- a m

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1 - a^{2}

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1 + a^{2}

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Solution

The correct option is C $1 - a^{2}$
Given Expression: $\frac{a^{2} m^{2} - 2 a m - 2 a^{3} m + (a^{2} m)^{2}}{(2 - a m)}$
$\Rightarrow \frac{a^{2} m^{2} + (a^{2} m)^{2} - 2 a m - 2 a^{3} m}{(2 - a m)} \Rightarrow \frac{(a^{2} m^{2}) (1 + a^{2}) - 2 a m (1 + a^{2})}{(2 - a m)} \Rightarrow \frac{(a^{2} m^{2} - 2 a m) (1 + a^{2})}{(2 - a m)} \Rightarrow \frac{(a m) (a m - 2) (1 + a^{2})}{(2 - a m)} \Rightarrow (- a m) (1 + a^{2})$

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