Question
Answer
$$(3-2x+25x^2)(x+21)^2-2(6x-16)(x+93)=25x^4+1048x^3+10932x^2-1840x+4299$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3-2x+25x^2)(x+21)^2-2(6x-16)(x+93)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3-2x+25x^2)(x^2+42x+441)-2(6x-16)(x+93) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}25x^4+1048x^3+10944x^2-756x+1323-(12x-32)(x+93) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}25x^4+1048x^3+10944x^2-756x+1323-(12x^2+1116x-32x-2976) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}25x^4+1048x^3+10944x^2-756x+1323-(12x^2+1084x-2976) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}25x^4+1048x^3+10944x^2-756x+1323-12x^2-1084x+2976 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}25x^4+1048x^3+10932x^2-1840x+4299\end{aligned} $$ | |
| ① | Find $ \left(x+21\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 21 }$. $$ \begin{aligned}\left(x+21\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 21 + \color{red}{21^2} = x^2+42x+441\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{3-2x+25x^2}\right) $ by each term in $ \left( x^2+42x+441\right) $. $$ \left( \color{blue}{3-2x+25x^2}\right) \cdot \left( x^2+42x+441\right) = \\ = 3x^2+126x+1323-2x^3-84x^2-882x+25x^4+1050x^3+11025x^2 $$ |
| ③ | Combine like terms: $$ \color{blue}{3x^2} + \color{red}{126x} +1323 \color{green}{-2x^3} \color{orange}{-84x^2} \color{red}{-882x} +25x^4+ \color{green}{1050x^3} + \color{orange}{11025x^2} = \\ = 25x^4+ \color{green}{1048x^3} + \color{orange}{10944x^2} \color{red}{-756x} +1323 $$Multiply $ \color{blue}{2} $ by $ \left( 6x-16\right) $ $$ \color{blue}{2} \cdot \left( 6x-16\right) = 12x-32 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{12x-32}\right) $ by each term in $ \left( x+93\right) $. $$ \left( \color{blue}{12x-32}\right) \cdot \left( x+93\right) = 12x^2+1116x-32x-2976 $$ |
| ⑤ | Combine like terms: $$ 12x^2+ \color{blue}{1116x} \color{blue}{-32x} -2976 = 12x^2+ \color{blue}{1084x} -2976 $$ |
| ⑥ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 12x^2+1084x-2976 \right) = -12x^2-1084x+2976 $$ |
| ⑦ | Combine like terms: $$ 25x^4+1048x^3+ \color{blue}{10944x^2} \color{red}{-756x} + \color{green}{1323} \color{blue}{-12x^2} \color{red}{-1084x} + \color{green}{2976} = \\ = 25x^4+1048x^3+ \color{blue}{10932x^2} \color{red}{-1840x} + \color{green}{4299} $$ |
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