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Ta thấy: (x + y )2 = x2 + 2.x.y + y2
=> 9x2 + y2 + 6xy = 9x2 + 6xy + y2
= (3x)2 + 2.3x.y + y2 = (3x + 4 )2
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3x^2-6xy+3y^2-12=3\left(x^2-2xy+y^2\right)-12=3\left(x-y\right)^2-12\ge-12\)
\(ĐTXR\Leftrightarrow x=y\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3x^2+6xy-48+3y^2=3\left[\left(x^2+2xy+y^2\right)-16\right]=3\left[\left(x+y\right)^2-16\right]=3\left(x+y-4\right)\left(x+y+4\right)\)
\(3x^2+6xy-48+3y^2\)
\(=3\left(x^2+2xy+y^2-16\right)\)
\(=3\left(x+y+4\right)\left(x+y-4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=x^3-8-128-x^3=-136\\ B=8x^3+27y^3-27x^3+8y^3=-19x^3+35y^3\)
\(A=\left(x-2\right)\left(x^2+2x+4\right)-\left(128+x^3\right)=x^3-8-128-x^3=-136\)
\(B=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)-\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)=8x^3+27y^3-27x^3+8y^3=-19x^3+35y^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
=\(\left(\sqrt{3}x-\sqrt{3}y\right)^2-12z=\left(\sqrt{3}x-\sqrt{3}y-\sqrt{12z}\right)\left(\sqrt{3}x-\sqrt{3}y+\sqrt{12z}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a,
$xy^2+x^2y+(-2xy^2)=xy^2-2xy^2+x^2y=-xy^2+x^2y$
b,
$12x^2y^3z^4+(-7x^2y^3z^4)=12x^2y^3z^4-7x^2y^3z^4=5x^2y^3z^4$
c,
$-6xy^3-(-6xy^3)+6x^3=-6xy^3+6xy^3+6x^3=0+6x^3=6x^3$
d,
$\frac{-x^2}{2}+\frac{7}{2}x^2+x=(\frac{7}{2}-\frac{1}{2})x^2+x$
$=3x^2+x$
e,
$2x^3+3x^3-\frac{1}{3}x^3=(2+3-\frac{1}{3})x^3=\frac{14}{3}x^3$
f,
$5xy^2+\frac{1}{2}xy^2+\frac{1}{4}xy^2=(5+\frac{1}{2}+\frac{1}{4})xy^2$
$=\frac{23}{4}xy^2$
Bai lam
\(3x^2-6xy=3x\left(x-2y\right)\)
=3x(x-2y)