Question
Answer
$$2(3x^2-14x+16)^2-(6x-14)(x^3-7x^2+16x-10)=12x^4-112x^3+390x^2-612x+372$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(3x^2-14x+16)^2-(6x-14)(x^3-7x^2+16x-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2(9x^4-84x^3+292x^2-448x+256)-(6x-14)(x^3-7x^2+16x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18x^4-168x^3+584x^2-896x+512-(6x^4-56x^3+194x^2-284x+140) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}18x^4-168x^3+584x^2-896x+512-6x^4+56x^3-194x^2+284x-140 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}12x^4-112x^3+390x^2-612x+372\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x^2-14x+16}\right) $ by each term in $ \left( 3x^2-14x+16\right) $. $$ \left( \color{blue}{3x^2-14x+16}\right) \cdot \left( 3x^2-14x+16\right) = 9x^4-42x^3+48x^2-42x^3+196x^2-224x+48x^2-224x+256 $$ |
| ② | Combine like terms: $$ 9x^4 \color{blue}{-42x^3} + \color{red}{48x^2} \color{blue}{-42x^3} + \color{green}{196x^2} \color{orange}{-224x} + \color{green}{48x^2} \color{orange}{-224x} +256 = \\ = 9x^4 \color{blue}{-84x^3} + \color{green}{292x^2} \color{orange}{-448x} +256 $$ |
| ③ | Multiply $ \color{blue}{2} $ by $ \left( 9x^4-84x^3+292x^2-448x+256\right) $ $$ \color{blue}{2} \cdot \left( 9x^4-84x^3+292x^2-448x+256\right) = 18x^4-168x^3+584x^2-896x+512 $$ Multiply each term of $ \left( \color{blue}{6x-14}\right) $ by each term in $ \left( x^3-7x^2+16x-10\right) $. $$ \left( \color{blue}{6x-14}\right) \cdot \left( x^3-7x^2+16x-10\right) = 6x^4-42x^3+96x^2-60x-14x^3+98x^2-224x+140 $$ |
| ④ | Combine like terms: $$ 6x^4 \color{blue}{-42x^3} + \color{red}{96x^2} \color{green}{-60x} \color{blue}{-14x^3} + \color{red}{98x^2} \color{green}{-224x} +140 = \\ = 6x^4 \color{blue}{-56x^3} + \color{red}{194x^2} \color{green}{-284x} +140 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x^4-56x^3+194x^2-284x+140 \right) = -6x^4+56x^3-194x^2+284x-140 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{18x^4} \color{red}{-168x^3} + \color{green}{584x^2} \color{orange}{-896x} + \color{blue}{512} \color{blue}{-6x^4} + \color{red}{56x^3} \color{green}{-194x^2} + \color{orange}{284x} \color{blue}{-140} = \\ = \color{blue}{12x^4} \color{red}{-112x^3} + \color{green}{390x^2} \color{orange}{-612x} + \color{blue}{372} $$ |
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