Tap the blue circles to see an explanation.
| $$ \begin{aligned}(65-x)(34x+2)^2-28(x-1)(xxx+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(65-x)(34x+2)^2-28(x-1)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(65-x)(1156x^2+136x+4)-28(x-1)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}75140x^2+8840x+260-1156x^3-136x^2-4x-(28x-28)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-1156x^3+75004x^2+8836x+260-(28x-28)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-1156x^3+75004x^2+8836x+260-(28x^4+84x-28x^3-84) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-1156x^3+75004x^2+8836x+260-28x^4-84x+28x^3+84 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-28x^4-1128x^3+75004x^2+8752x+344\end{aligned} $$ | |
| ① | $$ x x x = x^{1 + 1 + 1} = x^3 $$ |
| ② | Find $ \left(34x+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}{ 34x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(34x+2\right)^2 = \color{blue}{\left( 34x \right)^2} +2 \cdot 34x \cdot 2 + \color{red}{2^2} = 1156x^2+136x+4\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{65-x}\right) $ by each term in $ \left( 1156x^2+136x+4\right) $. $$ \left( \color{blue}{65-x}\right) \cdot \left( 1156x^2+136x+4\right) = 75140x^2+8840x+260-1156x^3-136x^2-4x $$Multiply $ \color{blue}{28} $ by $ \left( x-1\right) $ $$ \color{blue}{28} \cdot \left( x-1\right) = 28x-28 $$ |
| ④ | Combine like terms: $$ \color{blue}{75140x^2} + \color{red}{8840x} +260-1156x^3 \color{blue}{-136x^2} \color{red}{-4x} = -1156x^3+ \color{blue}{75004x^2} + \color{red}{8836x} +260 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{28x-28}\right) $ by each term in $ \left( x^3+3\right) $. $$ \left( \color{blue}{28x-28}\right) \cdot \left( x^3+3\right) = 28x^4+84x-28x^3-84 $$ |
| ⑥ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 28x^4+84x-28x^3-84 \right) = -28x^4-84x+28x^3+84 $$ |
| ⑦ | Combine like terms: $$ \color{blue}{-1156x^3} +75004x^2+ \color{red}{8836x} + \color{green}{260} -28x^4 \color{red}{-84x} + \color{blue}{28x^3} + \color{green}{84} = \\ = -28x^4 \color{blue}{-1128x^3} +75004x^2+ \color{red}{8752x} + \color{green}{344} $$ |