Question
Answer
$$(x-a-y+y)^2=a^2-2ax+x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-a-y+y)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-a+x)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2-2ax+x^2\end{aligned} $$ | |
| ① | Combine like terms: $$ x-a \, \color{blue}{ -\cancel{y}} \,+ \, \color{blue}{ \cancel{y}} \, = -a+x $$ |
| ② | Find $ \left(-a+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}{ a } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(-a+x\right)^2& \xlongequal{ S1 } \left(a-x\right)^2 \xlongequal{ S2 } \color{blue}{a^2} -2 \cdot a \cdot x + \color{red}{x^2} = \\[1 em] & = a^2-2ax+x^2\end{aligned} $$ |
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