Question
Multiply polynomial $ \, \color{blue}{ 7x^2 } \, $ by $ \, \color{orangered}{ -9x^6-3x^{12}-9x^{15} }$.
Answer
$$ \color{blue}{7x^2} \cdot \left( \color{orangered}{-9x^6-3x^{12}-9x^{15}} \right) = -63x^{17}-21x^{14}-63x^8 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 7x^2 \\ Q(x) &= -9x^{15}-3x^{12}-9x^6 \\ \end{aligned} $$We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \color{blue}{7x^2} \cdot \left( -9x^{15}-3x^{12}-9x^6 \right) &= \color{blue}{7x^2} \cdot \left( -9x^{15}\right) + \color{blue}{7x^2} \cdot \left( -3x^{12}\right) + \color{blue}{7x^2} \cdot \left( -9x^6\right) = \\ &= -63x^{17}-21x^{14}-63x^8 \end{aligned} $$This page was created using
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