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