Question
Answer
$$(-1-x)^2=x^2+2x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-1-x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1+2x+x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+2x+1\end{aligned} $$ | |
| ① | Find $ \left(-1-x\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply formula $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 1 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(-1-x\right)^2& \xlongequal{ S1 } \left(1+x\right)^2 \xlongequal{ S2 } \color{blue}{1^2} +2 \cdot 1 \cdot x + \color{red}{x^2} = \\[1 em] & = 1+2x+x^2\end{aligned} $$ |
| ② | Combine like terms: $$ x^2+2x+1 = x^2+2x+1 $$ |
This page was created using
Simplify polynomials calculator