Question

Para x + 3y = 21, qual o valor de x2 + 6xy + 9y2 ?

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Fatorac_{\!\!,}\tilde ao~do~trin\hat omio}\\\underline{\rm quadrado~perfeito:}\\\sf x^2+6xy+9y^2\\\sf \sqrt{x^2}=x~~~~\sqrt{9y^2}=3y\\\sf 2\cdot x\cdot3y=6xy\checkmark\implies \acute e~trin\hat o mio~quadrado~perfeito\\\sf forma~fatorada:(x+3y)^2\\\sf como~x+3y=21~vamos~substituir:\\\sf (x+3y)^2=21^2=441\\\sf portanto~x^2+6xy+9y^2\bigg|_{x+3y=21}=441\end{array}}$