Question
Multiply polynomial $ \, \color{blue}{ 7a^4-2a^2 } \, $ by $ \, \color{orangered}{ 4a-15 }$.
Answer
$$ \left( \color{blue}{7a^4-2a^2} \right) \cdot \left( \color{orangered}{4a-15} \right) = 28a^5-105a^4-8a^3+30a^2 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ 7a^4-2a^2}\right) \cdot \left( \color{orangered}{ 4a-15}\right) &= \underbrace{ \color{blue}{7a^4} \cdot \color{orangered}{4a} }_{\text{FIRST}} + \underbrace{ \color{blue}{7a^4} \cdot \left( \color{orangered}{-15} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-2a^2} \right) \cdot \color{orangered}{4a} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-2a^2} \right) \cdot \left( \color{orangered}{-15} \right) }_{\text{LAST}} = \\ &= 28a^5 + \left( -105a^4\right) + \left( -8a^3\right) + 30a^2 = \\ &= 28a^5 + \left( -105a^4\right) + \left( -8a^3\right) + 30a^2 = \\ &= 28a^5-105a^4-8a^3+30a^2; \end{aligned} $$This page was created using
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