Question
Answer
$$(n(b+1)+ar)^2=a^2r^2+2abnr+b^2n^2+2anr+2bn^2+n^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n(b+1)+ar)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1bn+n+ar)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}a^2r^2+2abnr+b^2n^2+2anr+2bn^2+n^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{n} $ by $ \left( b+1\right) $ $$ \color{blue}{n} \cdot \left( b+1\right) = bn+n $$ |
| ② | Multiply each term of $ \left( \color{blue}{bn+n+ar}\right) $ by each term in $ \left( bn+n+ar\right) $. $$ \left( \color{blue}{bn+n+ar}\right) \cdot \left( bn+n+ar\right) = b^2n^2+bn^2+abnr+bn^2+n^2+anr+abnr+anr+a^2r^2 $$ |
| ③ | Combine like terms: $$ b^2n^2+ \color{blue}{bn^2} + \color{red}{abnr} + \color{blue}{bn^2} +n^2+ \color{green}{anr} + \color{red}{abnr} + \color{green}{anr} +a^2r^2 = \\ = a^2r^2+ \color{red}{2abnr} +b^2n^2+ \color{green}{2anr} + \color{blue}{2bn^2} +n^2 $$ |
This page was created using
Simplify polynomials calculator