PP nhóm
1)x^2+x-y^2+y
2)4x^2-9y^2+4x-6y
3)x^2+x+y^2+y+2xy
4)-x^2+5x+2xy-5y-y^2
5)x^2-y^2+2x+1
6)x^2-1-y^2+2y
7)x^2+2xz-y^2+2uy+z^2-u^2
8)x^3+3x^2y+x+3xy^2+y+y^3
9)x^3+y(1-3x^2)+x(3y^2-1)-y^3
10)27x^3+27x^2+9x+1+x+1/3
Phân tích các đa thức sau thành nhân tử :
a, -x - y^2 + x^2 - y
b, x( x + y ) - 5x - 5y
c, x^2 - 5x + 5y - y^2
d, 5x^3 - 5x^2 y - 10x^2 + 10xy
e, 27x^3 - 8y^3
f, x^2 - y^2 - x - y
g, x^2 - y^2 - 2xy + y^2
h, x^2 - y^2 + 4 - 4x
i, x^3 + 3x^2 + 3x + 1 - 27z^3
k, 4x^2 + 4x - 9y^2 + 1
m, x^2 - 3x + xy - 3y
Giúp mình với mình đang cần rất gấp ạ
a, -x - y2 + x2 - y = (x2 - y2) - (x + y)
= (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
b, x( x + y ) - 5x - 5y = x(x + y) - 5(x + y)
= (x - 5)(x + y)
c, x2 - 5x + 5y - y2 = (x - y)(x + y) - 5(x - y)
= (x - y)(x + y - 5)
d, 5x3 - 5x2y - 10x2 + 10xy = 5x2(x - y) - 10x(x - y)
= 5x(x - y)(x - 2)
e, 27x3 - 8y3 = (3x - 2y)(9x2 + 6xy + 4y2)
f, x2 - y2 - x - y = (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
g, x2 - y2 - 2xy + y2 = (x2 - 2xy + y2) - y2
= (x - y)2 - y2
= (x - y - y)(x - y + y) = x(x - 2y)
h, x2 - y2 + 4 - 4x = (x2 - 4x + 4) - y2
= (x - 2)2 - y2
= (x - y - 2)(x + y - 2)
i, x3 + 3x2 + 3x + 1 - 27z3 = (x + 1)3 - 27z3
= (x+1-3z)(x2+2x+1+3xz+3z+9z2)
k, 4x2 + 4x - 9y2 + 1 = (2x + 1)2 - 9y2
= (2x - 3y + 1)(2x + 3y + 1)
m, x2 - 3x + xy - 3y = x(x - 3) + y(x - 3)
= (x - 3)(x + y)
Tìm x,y,z biết: a) x^2+y^2-4x+4y+8=0 b) 5x^2-4xy+y^2=0 c) x^2+2y^2+z^2-2xy-2y-4z+5=0 d) 3x^2+3y^2+3xy-3x+3y+3=0 e) 2x^2+y^2+2z^2-2xy-2xz+2yz-2z-2z-2x+2=0
a) x2+y2-4x+4y+8=0
⇔ (x-2)2+(y+2)2=0
\(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\y+2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-2\end{matrix}\right.\)
b)5x2-4xy+y2=0
⇔ x2+(2x-y)2=0
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\2x-y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\)
c)x2+2y2+z2-2xy-2y-4z+5=0
⇔ (x-y)2+(y-1)2+(z-2)2=0
\(\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\y-1=0\\z-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=y=1\\z=2\end{matrix}\right.\)
b: Ta có: \(5x^2-4xy+y^2=0\)
\(\Leftrightarrow x^2-\dfrac{4}{5}xy+y^2=0\)
\(\Leftrightarrow x^2-2\cdot x\cdot\dfrac{2}{5}y+\dfrac{4}{25}y^2+\dfrac{21}{25}y^2=0\)
\(\Leftrightarrow\left(x-\dfrac{2}{5}y\right)^2+\dfrac{21}{25}y^2=0\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\)
d)3x2+3y2+3xy-3x+3y+3=0
⇔ 6x2+6y2+6xy-6x+6y+6=0
⇔ 3(x+y)2+3(x-1)2+3(y+1)2=0
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\x-1=0\\y+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)
Phân tích đa thức sau thành nhân tử :
a, -x - y^2 + x^2 - y
b, x( x + y ) - 5x - 5y
c,x^2 - 5x + 5y - y^2
d, 5x^3 - 5x^2 y - 10x^2 + 10xy
e,27x^3 - 8y^3
f, x^2 - y^2 - x - y
g, x^2 - y^2 - 2xy + y^2
h, x^2 - y^2 + 4 - 4x
i, x^6 - y^6
k, x^3 + 3x^2 + 3x + 1 - 27z^3
l, 4x^2 + 4x - 9y^2 + 1
m, x^2 - 3x + xy - 3y
Giúp mình với mình đang cần rất gấp ạ
a) \(-x-y^2+x^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right).1\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b) \(x\left(x+y\right)-5x-5y\)
\(=x\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x+y\right)\left(x-5\right)\)
c) \(x^2-5x+5y-y^2\)
\(=\left(x^2-y^2\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
d) \(5x^3-5x^2y-10x^2+10xy\)
\(=5x\left(x^2-xy-2x+2y\right)\)
\(=5x\left[x\left(x-y\right)-2\left(x-y\right)\right]\)
\(=5x\left(x-y\right)\left(x-2\right)\)
e) \(27x^3-8y^3\)
\(=\left(3x\right)^3-\left(2y\right)^3\)
\(=\left(3x-2y\right)\left[\left(3x\right)^2+3x2y+\left(2y\right)^2\right]\)
\(=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)
f) \(x^2-y^2-x-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
g) \(x^2-y^2-2xy+y^2\)
\(=\left(x^2-2xy+y^2\right)-y^2\)
\(=\left(x-y\right)^2-y^2\)
\(=\left(x-y-y\right)\left(x-y+y\right)\)
\(=\left(x-y^2\right)x\)
h) \(x^2-y^2+4-4x\)
\(=\left(x^2-4x+4\right)-y^2\)
\(=\left(x^2-2.2x+2^2\right)-y^2\)
\(=\left(x-2\right)^2-y^2\)
\(=\left(x-2-y\right)\left(x-2+y\right)\)
i) \(x^6-y^6\)
\(=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left[\left(x-y\right)\left(x^2+xy+y^2\right)\right]\left[\left(x+y\right)\left(x^2-xy+y^2\right)\right]\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
PP nhóm
1)2xy+3z+6y+xz
2)x^4-9x^3+x^2-9x
3)x^2-xy+x-y
4)xz+yz-5(x+y)
5)3x^2-3xy-5x+5y
6)x^2+4x-y^2+4
7)3x^2+6xy+3y^2-3z^2
8)x^2-2xy+y^2-z^2+2zt-t^2
1)2xy+3z+6y+xz
= x(2y + z) + 3(z + 2y)
= (x + 3)(2y + z)
2)x^4-9x^3+x^2-9x
= x^2(x^2 + 1) - 9x(x^2 + 1)
= (x^2 + 1)(x^2 - 9x)
= x(x - 9)(x^2 + 1)
3)x^2-xy+x-y
= x(x - y) + (x - y)
= (x + 1)(x - y)
4)xz+yz-5(x+y)
= z(x + y) - 5(x + y)
= (z - 5)(x + y)
5)3x^2-3xy-5x+5y
= 3x(x - y) - 5(x - y)
= (3x - 5)(x - y)
6)x^2+4x-y^2+4y
= (x - y)(x + y) + 4(x + y)
= (x - y + 4)(x + y)
a) x^2+2xy+y^2-16
b) 3x^2+5x-3xy-5y
c) 4x^2-6x^3y-2x^2+8x
d) x^2-4-2xy+y^2
e) x^3-4x^2-12x+27
g) 3x^2-18x+27
h) x^2-y^2-z^2-2yz
k) 4x^2(x-6)+9y^2(6-x)
l)6xy+5x-5y-3x^2-3y^2
a) x^2+2xy+y^2-16
=(x+y)2-16
=(x+y-4)(x+y+4)
b) 3x^2+5x-3xy-5y
=(3x2-3xy)+(5x-5y)
=3x(x-y)+5(x-y)
=(x-y)(3x+5)
c) 4x^2-6x^3y-2x^2+8x
ko bik hoặc sai đề
d) x^2-4-2xy+y^2
=(x-y)2-4
=(x-y+2)(x-y-2)
e) x^3-4x^2-12x+27
=sai đề
g) 3x^2-18x+27
=3(x2-6x+9)
=3(x-3)2
h) x^2-y^2-z^2-2yz
=x2-(y2+z2+2yx)
=x2-(y+z)2
=(x-y-z)(x+y+z)
k) 4x^2(x-6)+9y^2(6-x)
=4x2(x-6)-9y2(x-6)
=(x-6)(4x2-9y2)
=(x-6)(2x-3y)(2x+3y)
l)6xy+5x-5y-3x^2-3y^2
=(5x-5y)+(-3x2+6xy-3y2)
=5(x-y)-3(x2-2xy+y2)
=5(x-y)-3(x-y)2
=(x-y)(5-3(x-y))
=(x-y)(5-3x+3y)
A.5x^2y^3-25x^3y^4+10x^3y^3
B.12x^2y-18xy^2-30y^2
C.5(x-y)-y(x-y)
D.y(x-z)+7(z-x)
E.27x^2(y-1)-9x^3(1-y)
F.36-12x+x^2
G.x^2+2xy+y^2-xz-yz
H.x^4+64
I.27x^2(y-1)-9x^3(1-y)
K.36-12x+x^2
M.-4x^2+4x-1
N.x^2+5x+6
P.x^2-x-6
Q.x^4-5x^2+4
1/ tìm GTNN
4x^2+y^2-4x-2y+3
X^2+y^2+2*(x-2y)y+6
2 phân tich đa thức thành nhân tử
(x+y)^2-25(x+y)+24
2x^3y-2xy-4xy-2xy
y^2 +3xy+3y^2 (y#0)
(x^2+4x+8)^2-3x(x^2+4x+8) +x^2
x^3-y^3-3x+3y
x^4+6x^2+13x^2+12x+4
phân tích thành nhân tử
`3x^2 -3xy-5x+5y`
`2x^3 y-2xy^3 -4xy^2 -2xy`
`x^2 -1+2x-y^2`
`x^2 +4x-2xy-4y+4y^2`
`x^3 -2x^2 +x`
`2x^2 +4x+2-2y^2`
a) \(3x^2-3xy-5x+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
b) \(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
c) \(x^2+1+2x-y^2\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
d) \(x^2+4x-2xy-4y+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)^2+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+4\right)\)
e) \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
f) \(2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x^2+2x+1\right)+y^2\right]\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x-y+1\right)\left(x+y+1\right)\)
a: =3x(x-y)-5(x-y)
=(x-y)(3x-5)
b: \(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
d:
Sửa đề: x^2+4x-2xy-4y+y^2
=x^2-2xy+y^2+4x-4y
=(x-y)^2+4(x-y)
=(x-y)(x-y+4)
e: =x(x^2-2x+1)
=x(x-1)^2
f: =2(x^2+2x+1-y^2)
=2[(x+1)^2-y^2]
=2(x+1+y)(x+1-y)
Phân tích các đa thức sau đây thành nhân tử
a, 36x^2 - ( 3x -2 ) ^2
b, 16(4x+5)^5 - 25 (2x+2)^2
c, ( x - y + 4 )^2
d, (x+1)^4 - (x-1)^4
e, 16x^2 - 24xy + 9y^2
f, -x^4/4 + 2x^2y^3 - 4y^6
g , 64x^3 +1
h, x^3y^6z^9 - 125
k, 27x^6 - 8x^3
I , x^6 - y^6
m, 27x^3 - 54x^2y + 36xy^2 - 8y^3
n, y^9 - 9x^2y^6 + 27x^4y^3 - 27x^6
làm ơn giải chi tiết giúp mik vs ạ , cảm ơn
a: =(6x)^2-(3x-2)^2
=(6x-3x+2)(6x+3x-2)
=(9x-2)(3x+2)
d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)
\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)
=8x(x^2+1)
e: =(4x)^2-2*4x*3y+(3y)^2
=(4x-3y)^2
f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)
\(=-\left(\dfrac{1}{2}x^2-2y^3\right)^2\)
g: =(4x)^3+1^3
=(4x+1)(16x^2-4x+1)
k: =x^3(27x^3-8)
=x^3(3x-2)(9x^2+6x+4)
l: =(x^3-y^3)(x^3+y^3)
=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)