Question 38: Polynomial analysis \(\begin{aligned} &15 a^{m+2} b-45 a^{m} b\left(m \in \mathbb{N}^{*}\right ) \end{aligned}\) to factor:
\(\begin{aligned} &15 a^{m+2} b-45 a^{m} b\left(m \in \mathbb{N}^{*}\right) \\ &=15 a^{ m} \cdot a^{2} b-45 a^{m} b \quad\left(m \in \mathbb{N}^{*}\right) \\ &=15 a^{m} b\ left(a^{2}-3\right) \quad\left(m \in \mathbb{N}^{*}\right) \\ &=15 a^{m} b(a-\sqrt{3 })(a+\sqrt{3})\left(m \in \mathbb{N}^{*}\right) . \end{aligned}\)
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