Question
Answer
$$4t^6+(3t^2+a)a-(t^2+a)(4t^2+a)=4t^6-4t^4-2at^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4t^6+(3t^2+a)a-(t^2+a)(4t^2+a)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4t^6+3at^2+a^2-(4t^4+at^2+4at^2+a^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4t^6+3at^2+a^2-(4t^4+5at^2+a^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4t^6+3at^2+a^2-4t^4-5at^2-a^2 \xlongequal{ } \\[1 em] & \xlongequal{ }4t^6+3at^2+ \cancel{a^2}-4t^4-5at^2 -\cancel{a^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4t^6-4t^4-2at^2\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{3t^2+a}\right) \cdot a = 3at^2+a^2 $$ Multiply each term of $ \left( \color{blue}{t^2+a}\right) $ by each term in $ \left( 4t^2+a\right) $. $$ \left( \color{blue}{t^2+a}\right) \cdot \left( 4t^2+a\right) = 4t^4+at^2+4at^2+a^2 $$ |
| ② | Combine like terms: $$ 4t^6+3at^2+a^2 = 4t^6+3at^2+a^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4t^4+5at^2+a^2 \right) = -4t^4-5at^2-a^2 $$ |
| ④ | Combine like terms: $$ 4t^6+ \color{blue}{3at^2} + \, \color{red}{ \cancel{a^2}} \,-4t^4 \color{blue}{-5at^2} \, \color{red}{ -\cancel{a^2}} \, = 4t^6-4t^4 \color{blue}{-2at^2} $$ |
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