Tap the blue circles to see an explanation.
$$ \begin{aligned}(x+28)(x+14)(x+5)^2(x-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x+28)(x+14)(x^2+10x+25)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+14x+28x+392)(x^2+10x+25)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^2+42x+392)(x^2+10x+25)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(x^4+52x^3+837x^2+4970x+9800)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}x^5+42x^4+317x^3-3400x^2-39900x-98000\end{aligned} $$ | |
① | Find $ \left(x+5\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}{ 5 }$. $$ \begin{aligned}\left(x+5\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 5 + \color{red}{5^2} = x^2+10x+25\end{aligned} $$ |
② | Multiply each term of $ \left( \color{blue}{x+28}\right) $ by each term in $ \left( x+14\right) $. $$ \left( \color{blue}{x+28}\right) \cdot \left( x+14\right) = x^2+14x+28x+392 $$ |
③ | Combine like terms: $$ x^2+ \color{blue}{14x} + \color{blue}{28x} +392 = x^2+ \color{blue}{42x} +392 $$ |
④ | Multiply each term of $ \left( \color{blue}{x^2+42x+392}\right) $ by each term in $ \left( x^2+10x+25\right) $. $$ \left( \color{blue}{x^2+42x+392}\right) \cdot \left( x^2+10x+25\right) = \\ = x^4+10x^3+25x^2+42x^3+420x^2+1050x+392x^2+3920x+9800 $$ |
⑤ | Combine like terms: $$ x^4+ \color{blue}{10x^3} + \color{red}{25x^2} + \color{blue}{42x^3} + \color{green}{420x^2} + \color{orange}{1050x} + \color{green}{392x^2} + \color{orange}{3920x} +9800 = \\ = x^4+ \color{blue}{52x^3} + \color{green}{837x^2} + \color{orange}{4970x} +9800 $$ |
⑥ | Multiply each term of $ \left( \color{blue}{x^4+52x^3+837x^2+4970x+9800}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{x^4+52x^3+837x^2+4970x+9800}\right) \cdot \left( x-10\right) = \\ = x^5-10x^4+52x^4-520x^3+837x^3-8370x^2+4970x^2-49700x+9800x-98000 $$ |
⑦ | Combine like terms: $$ x^5 \color{blue}{-10x^4} + \color{blue}{52x^4} \color{red}{-520x^3} + \color{red}{837x^3} \color{green}{-8370x^2} + \color{green}{4970x^2} \color{orange}{-49700x} + \color{orange}{9800x} -98000 = \\ = x^5+ \color{blue}{42x^4} + \color{red}{317x^3} \color{green}{-3400x^2} \color{orange}{-39900x} -98000 $$ |