Question
Answer
$$(x+1)^3(x^2+x+1)=x^5+4x^4+7x^3+7x^2+4x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)^3(x^2+x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^3+3x^2+3x+1)(x^2+x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^5+4x^4+7x^3+7x^2+4x+1\end{aligned} $$ | |
| ① | Find $ \left(x+1\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = x $ and $ B = 1 $. $$ \left(x+1\right)^3 = x^3+3 \cdot x^2 \cdot 1 + 3 \cdot x \cdot 1^2+1^3 = x^3+3x^2+3x+1 $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^3+3x^2+3x+1}\right) $ by each term in $ \left( x^2+x+1\right) $. $$ \left( \color{blue}{x^3+3x^2+3x+1}\right) \cdot \left( x^2+x+1\right) = x^5+x^4+x^3+3x^4+3x^3+3x^2+3x^3+3x^2+3x+x^2+x+1 $$ |
| ③ | Combine like terms: $$ x^5+ \color{blue}{x^4} + \color{red}{x^3} + \color{blue}{3x^4} + \color{green}{3x^3} + \color{orange}{3x^2} + \color{green}{3x^3} + \color{blue}{3x^2} + \color{red}{3x} + \color{blue}{x^2} + \color{red}{x} +1 = \\ = x^5+ \color{blue}{4x^4} + \color{green}{7x^3} + \color{blue}{7x^2} + \color{red}{4x} +1 $$ |
This page was created using
Simplify polynomials calculator