Question
Answer
$$(5x+1)^4=625x^4+500x^3+150x^2+20x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x+1)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}625x^4+500x^3+150x^2+20x+1\end{aligned} $$ | |
| ① | $$ (5x+1)^4 = (5x+1)^2 \cdot (5x+1)^2 $$ |
| ② | Find $ \left(5x+1\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(5x+1\right)^2 = \color{blue}{\left( 5x \right)^2} +2 \cdot 5x \cdot 1 + \color{red}{1^2} = 25x^2+10x+1\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{25x^2+10x+1}\right) $ by each term in $ \left( 25x^2+10x+1\right) $. $$ \left( \color{blue}{25x^2+10x+1}\right) \cdot \left( 25x^2+10x+1\right) = 625x^4+250x^3+25x^2+250x^3+100x^2+10x+25x^2+10x+1 $$ |
| ④ | Combine like terms: $$ 625x^4+ \color{blue}{250x^3} + \color{red}{25x^2} + \color{blue}{250x^3} + \color{green}{100x^2} + \color{orange}{10x} + \color{green}{25x^2} + \color{orange}{10x} +1 = \\ = 625x^4+ \color{blue}{500x^3} + \color{green}{150x^2} + \color{orange}{20x} +1 $$ |
This page was created using
Simplify polynomials calculator