Question
Answer
$$(3+25x^2)(8x+2)^2-2(x-16x+93+x^4)=1598x^4+800x^3+292x^2+126x-174$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+25x^2)(8x+2)^2-2(x-16x+93+x^4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3+25x^2)(8x+2)^2-2(x^4-15x+93) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3+25x^2)(64x^2+32x+4)-2(x^4-15x+93) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}192x^2+96x+12+1600x^4+800x^3+100x^2-(2x^4-30x+186) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}1600x^4+800x^3+292x^2+96x+12-(2x^4-30x+186) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}1600x^4+800x^3+292x^2+96x+12-2x^4+30x-186 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}1598x^4+800x^3+292x^2+126x-174\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{x} \color{blue}{-16x} +93+x^4 = x^4 \color{blue}{-15x} +93 $$ |
| ② | Find $ \left(8x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 8x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(8x+2\right)^2 = \color{blue}{\left( 8x \right)^2} +2 \cdot 8x \cdot 2 + \color{red}{2^2} = 64x^2+32x+4\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{3+25x^2}\right) $ by each term in $ \left( 64x^2+32x+4\right) $. $$ \left( \color{blue}{3+25x^2}\right) \cdot \left( 64x^2+32x+4\right) = 192x^2+96x+12+1600x^4+800x^3+100x^2 $$Multiply $ \color{blue}{2} $ by $ \left( x^4-15x+93\right) $ $$ \color{blue}{2} \cdot \left( x^4-15x+93\right) = 2x^4-30x+186 $$ |
| ④ | Combine like terms: $$ \color{blue}{192x^2} +96x+12+1600x^4+800x^3+ \color{blue}{100x^2} = 1600x^4+800x^3+ \color{blue}{292x^2} +96x+12 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^4-30x+186 \right) = -2x^4+30x-186 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{1600x^4} +800x^3+292x^2+ \color{red}{96x} + \color{green}{12} \color{blue}{-2x^4} + \color{red}{30x} \color{green}{-186} = \\ = \color{blue}{1598x^4} +800x^3+292x^2+ \color{red}{126x} \color{green}{-174} $$ |
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