Multiply polynomial $ \, \color{blue}{ 2q^7+3q^7 } \, $ by $ \, \color{orangered}{ -6q^2+9 }$.

$$ \left( \color{blue}{2q^7+3q^7} \right) \cdot \left( \color{orangered}{-6q^2+9} \right) = -30q^9+45q^7 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 5q^7 \\ Q(x) &= -6q^2+9 \\ \end{aligned} $$

We can use distribution property to multiply the polynomial by the monomial.

$$ \begin{aligned} \color{blue}{5q^7} \cdot \left( -6q^2+9 \right) &= \color{blue}{5q^7} \cdot \left( -6q^2\right) + \color{blue}{5q^7} \cdot 9 = \\ &= -30q^9+45q^7 \end{aligned} $$

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