Question
Answer
$$(7x+1)^4=2401x^4+1372x^3+294x^2+28x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7x+1)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2401x^4+1372x^3+294x^2+28x+1\end{aligned} $$ | |
| ① | $$ (7x+1)^4 = (7x+1)^2 \cdot (7x+1)^2 $$ |
| ② | Find $ \left(7x+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}{ 7x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(7x+1\right)^2 = \color{blue}{\left( 7x \right)^2} +2 \cdot 7x \cdot 1 + \color{red}{1^2} = 49x^2+14x+1\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{49x^2+14x+1}\right) $ by each term in $ \left( 49x^2+14x+1\right) $. $$ \left( \color{blue}{49x^2+14x+1}\right) \cdot \left( 49x^2+14x+1\right) = 2401x^4+686x^3+49x^2+686x^3+196x^2+14x+49x^2+14x+1 $$ |
| ④ | Combine like terms: $$ 2401x^4+ \color{blue}{686x^3} + \color{red}{49x^2} + \color{blue}{686x^3} + \color{green}{196x^2} + \color{orange}{14x} + \color{green}{49x^2} + \color{orange}{14x} +1 = \\ = 2401x^4+ \color{blue}{1372x^3} + \color{green}{294x^2} + \color{orange}{28x} +1 $$ |
This page was created using
Simplify polynomials calculator