Question
Multiply polynomial $ \, \color{blue}{ -5x^2+7 } \, $ by $ \, \color{orangered}{ -5x^2-7 }$.
Answer
$$ \left( \color{blue}{-5x^2+7} \right) \cdot \left( \color{orangered}{-5x^2-7} \right) = 25x^4-49 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ -5x^2+7}\right) \cdot \left( \color{orangered}{ -5x^2-7}\right) &= \underbrace{ \left( \color{blue}{-5x^2} \right) \cdot \left( \color{orangered}{-5x^2} \right) }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-5x^2} \right) \cdot \left( \color{orangered}{-7} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{7} \cdot \left( \color{orangered}{-5x^2} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{7} \cdot \left( \color{orangered}{-7} \right) }_{\text{LAST}} = \\ &= 25x^4 + 35x^2 + \left( -35x^2\right) + \left( -49\right) = \\ &= 25x^4 + 35x^2 + \left( -35x^2\right) + \left( -49\right) = \\ &= 25x^4-49; \end{aligned} $$This page was created using
Polynomial Operations Calculator