Question
Answer
$$(ab-1)^4=a^4b^4-4a^3b^3+6a^2b^2-4ab+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(ab-1)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}a^4b^4-4a^3b^3+6a^2b^2-4ab+1\end{aligned} $$ | |
| ① | $$ (ab-1)^4 = (ab-1)^2 \cdot (ab-1)^2 $$ |
| ② | Find $ \left(ab-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}{ ab } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(ab-1\right)^2 = \color{blue}{\left( ab \right)^2} -2 \cdot ab \cdot 1 + \color{red}{1^2} = a^2b^2-2ab+1\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{a^2b^2-2ab+1}\right) $ by each term in $ \left( a^2b^2-2ab+1\right) $. $$ \left( \color{blue}{a^2b^2-2ab+1}\right) \cdot \left( a^2b^2-2ab+1\right) = \\ = a^4b^4-2a^3b^3+a^2b^2-2a^3b^3+4a^2b^2-2ab+a^2b^2-2ab+1 $$ |
| ④ | Combine like terms: $$ a^4b^4 \color{blue}{-2a^3b^3} + \color{red}{a^2b^2} \color{blue}{-2a^3b^3} + \color{green}{4a^2b^2} \color{orange}{-2ab} + \color{green}{a^2b^2} \color{orange}{-2ab} +1 = \\ = a^4b^4 \color{blue}{-4a^3b^3} + \color{green}{6a^2b^2} \color{orange}{-4ab} +1 $$ |
This page was created using
Simplify polynomials calculator