x^2-2xy+y^2-36
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\(36+2xy-x^2-y^2\)
\(=36-\left(x^2-2xy+y^2\right)\)
\(=6^2-\left(x-y\right)^2\)
\(=\left(6-x+y\right)\left(6+x-y\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-36+2xy+y^2=\left(x^2+2xy+y^2\right)-36=\left(x+y\right)^2-6^2=\left(x+y+6\right)\left(x+y-6\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2xy-x^2-y^2+36\)
\(=-\left(x^2+2xy-y^2\right)+36\)
\(=-\left(x^2-2xy+y^2\right)+36\)
\(=-\left(x-y\right)^2+6^2\)
\(=-\left(x-y+6\right).\left(x-y-6\right)\)
Ta có: \(2xy-x^2-y^2+36=-\left(x^2-2xy+y^2-36\right)\)
\(=-\left[\left(x-y\right)^2-36\right]=-\left(x-y-6\right)\left(x-y+6\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x2 +2xy + x + 2y
= (x2 +2xy) + (x + 2y)
= x(x + 2y) + (x + 2y)
= (x + 2y)(x + 1)
b) 7x2 - 7xy - 5x + 5y
= (7x2 - 7xy) - (5x - 5y)
= 7x(x - y) - 5(x - y)
= (x - y)(7x - 5)
c) 3(x + 2) - y(x + 2)
= (x + 2)(3 - y)
d) 5(x - 3) + y(3 - x)
= 5(x - 3) - y(x - 3)
= (x - 3)(5 - y)
e) (x2 - 8)2 + 36
= x4 - 16x2 + 64 + 36
= x4 - 16x2 + 100
= x4 + 20x2 - 36x2 + 100
= (x4 + 20x2 + 100) - 36x2
= (x2 + 10)2 - (6x)2
= (x2 + 10 - 6x)(x2 + 10 + 6x)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(Q=3xy\left(x+3y\right)-2xy\left(x+4y\right)-x^2\left(y-1\right)+y^2\left(1-x\right)+36\)\(\Leftrightarrow Q=3x^2y+9xy^2-2x^2y-8xy^2-x^2y+x^2+y^2-xy^2+36\)\(\Leftrightarrow Q=\left(3x^2y-2x^2y-x^2y\right)+\left(9xy^2-8xy^2-xy^2\right)+x^2+y^2+36\)\(\Leftrightarrow Q=x^2+y^2+36\ge36\forall x;y\)
Dấu " = " xảy ra
\(\Leftrightarrow\left\{{}\begin{matrix}x^2=0\\y^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\)
Vậy Min Q là : \(36\Leftrightarrow x=y=0\)
x2-2xy+y2-36
= (x2-2xy+y2)-62
= (x-y)2-62
= (x-y+6)(x-y-6)
sai một tí nha