Question
Answer
$$(x+5)^2(20x^2+40x-9)=20x^4+240x^3+891x^2+910x-225$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+5)^2(20x^2+40x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+10x+25)(20x^2+40x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}20x^4+240x^3+891x^2+910x-225\end{aligned} $$ | |
| 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^2+10x+25}\right) $ by each term in $ \left( 20x^2+40x-9\right) $. $$ \left( \color{blue}{x^2+10x+25}\right) \cdot \left( 20x^2+40x-9\right) = \\ = 20x^4+40x^3-9x^2+200x^3+400x^2-90x+500x^2+1000x-225 $$ |
| ③ | Combine like terms: $$ 20x^4+ \color{blue}{40x^3} \color{red}{-9x^2} + \color{blue}{200x^3} + \color{green}{400x^2} \color{orange}{-90x} + \color{green}{500x^2} + \color{orange}{1000x} -225 = \\ = 20x^4+ \color{blue}{240x^3} + \color{green}{891x^2} + \color{orange}{910x} -225 $$ |
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