Question

phân tích đa thức thành nhân tử :

x² + 2xy + 7x + 7y + y² + 10

Answer 1

\(x^2+2xy+y^2+7x+7y+10\)

\(=\left(x+y\right)^2+7\left(x+y\right)+10\)

\(=\left(x+y\right)^2+2\times\dfrac{7}{2}\times\left(x+y\right)+\dfrac{49}{4}-\dfrac{49}{4}+10\)

\(=\left(x+y+\dfrac{7}{2}\right)^2-\dfrac{9}{4}\)

\(=\left(x+y+\dfrac{7}{2}-\dfrac{3}{2}\right)\times\left(x+y+\dfrac{7}{2}+\dfrac{3}{2}\right)\)

\(=\left(x+y+2\right)\times\left(x+y+5\right)\)

Answer 2

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)

Answer 3

\(\Leftrightarrow\)(x²+2xy+y²)+(7x+7y)+10

\(\Leftrightarrow\)(x+y)²+7(x+y)+10

\(\Leftrightarrow\)(x+y)+(x+y+7)+10