phân tích đa thức thành nhân tử : y^2.( x^2 + y ) - zx^2 - zy
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KC
2
25 tháng 7 2021
Ta có: \(y^2\left(x^2+y\right)-zx^2-zy\)
\(=y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
\(=\left(x^2+y\right)\left(y^2-z\right)\)
T
2
LT
13 tháng 10 2017
a. -\(-16x^2+8xy-y^2+49\)
= \(\left(-\left(4x\right)^2+8xy-y^2\right)+49\)
= \(-\left(\left(4x^2\right)-8xy+y^2\right)+49\)
= \(-\left(4x-y\right)^2+49\)
b. \(y^2\left(x^2+y\right)-zx^2-zy\)
= \(y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
= \(\left(x^2+y\right)\left(y^2-z\right)\)
13 tháng 10 2017
_16x2+8xy_y2+49
=( _(4x)2+2 × 4 × xy _ y2 )+ 72
= _((4x)2_ 2×4×x × xy +y2)+72
= _(4x_y)2+72
=72_(4x_y)2
= (7_(4x_y))×(7+(4x_y))
= (7_4x+y)×(7+4x_y)
2)y2×(x2+y)_zx2_zy
=y×(x2+y)_z(x2+y)
= ( x2+y)×(y_z)
MC
0
KN
13 tháng 10 2019
a) \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4\right)^2-\left(7x\right)^2\)
\(=\left(12x-4\right)\left(-2x-4\right)\)
\(=-6\left(3x-1\right)\left(x+2\right)\)
c) \(x^2-y^2-x+y\)
\(=\left(x+y\right)\left(x-y\right)-\left(x-y\right)\)
\(=\left(x+y-1\right)\left(x-y\right)\)
d)\(4x^2-9y^2+4x-6y\)
\(=\left(2x-3y\right)\left(2x+3y\right)+2\left(2y-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
KN
13 tháng 10 2019
e) \(-x^2+5x+2xy-5y-y^2\)
\(=-\left(x^2-2xy+y^2\right)+\left(5x-5y\right)\)
\(=-\left(x-y\right)^2+5\left(x-y\right)\)
\(=\left(x-y\right)\left(y-x+5\right)\)
f) \(y^2\left(x^2+y\right)-zx^2-zy\)
\(=y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
\(=\left(y^2-z\right)\left(x^2+y\right)\)
11 tháng 7 2021
\(2\left(xy+yz+zx\right)-x^2-y^2-z^2\)
\(2xy+2yz+2zx-x^2-y^2-z^2\)
\(-\left(x^2+y^2+z^2-2xy-2yz-2xz\right)\)
\(-\left(x+y+z\right)^2\)
NN
0
12 tháng 10 2021
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
KY
16 tháng 9 2019
\(x\left(y^2-z^2\right)+y\left(z^2-x^2\right)+z\left(x^2-y^2\right)\)
\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2\)
\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2-xyz+xyz\)
\(=\left(yz^2-xz^2-xyz+x^2z\right)-\left(zy^2-xyz-xy^2+x^2y\right)\)
\(=z\left(yz-xz-xy+x^2\right)-y\left(zy-xz-xy+x^2\right)\)
\(=\left(z-y\right)\left(yz-xz-xy+x^2\right)\)
\(=\left(z-y\right)\left[y\left(z-x\right)-x\left(z-x\right)\right]\)
\(=\left(z-y\right)\left(y-x\right)\left(z-x\right)\)
Ta có : y2( x2 + y ) - zx2 - zy
= y2( x2 + y ) - z( x2 + y )
= ( x2 + y )( y2 - z )
\(y^2\left(x^2+y\right)-zx^2-zy\)
\(=y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
\(=\left(x^2+y\right)\left(y^2-z\right)\)