Question

A expressão ( x + y )² resulta em: 

a) x² - 2xy + y²

b) x² + 2xy + y²

c) x² - xy + y²

d) x² + xy + y²​

Answer 1

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$\boxed{\begin{array}{l}\underline{\rm por~produto~not\acute aveis\!:}\\\sf (x+y)^2=x^2+2xy+y^2\\\underline{\rm por~bin\hat omio~de~Newton\!:}\\\sf(x+y)^2=\displaystyle\binom{2}{0} x^2+\binom{2}{1}x^{2-1}y+\binom{2}{2}x^{1-1}y^{2}\\\underline{\tt c\acute alculos~auxiliares:}\\\displaystyle\sf\binom{2}{0}=\dfrac{2!}{0!(2-0)!}=\dfrac{\backslash\!\!\!\!\!2!}{1\cdot\backslash\!\!\!\!2!}=1\\\displaystyle\sf \binom{2}{2}=\binom{2}{0}=1\\\displaystyle\sf\binom{2}{1}=\dfrac{2!}{1!\cdot(2-1)!}=2\end{array}}$

$\large\boxed{\begin{array}{l}\sf portanto~\\\sf (x+y)^2=x^2+2xy+y^2\end{array}}$