\(x^2+2xy+y^2+7x+7y+10\)
\(=\left(x+y\right)^2+7\left(x+y\right)+10\)
\(=\left(x+y\right)^2+2\times\dfrac{7}{2}\times\left(x+y\right)+\dfrac{49}{4}-\dfrac{49}{4}+10\)
\(=\left(x+y+\dfrac{7}{2}\right)^2-\dfrac{9}{4}\)
\(=\left(x+y+\dfrac{7}{2}-\dfrac{3}{2}\right)\times\left(x+y+\dfrac{7}{2}+\dfrac{3}{2}\right)\)
\(=\left(x+y+2\right)\times\left(x+y+5\right)\)
x2+2xy+7x+7y+y2+10
=x2+y2+12,25+2xy+7x+7y-2,25
=(x+y+3,5)2-(1,5)2
=(x+y+3,5+1,5)(x+y+3,5-1,5)
=(x+y+5)(x+y+2)
\(\Leftrightarrow\)(x2+2xy+y2)+(7x+7y)+10
\(\Leftrightarrow\)(x+y)2+7(x+y)+10
\(\Leftrightarrow\)(x+y)+(x+y+7)+10
