Phân tích đa thức thành nhân tử
a) x6_ x4-9x3-9x2
b) ( ab-xy)2-(bx-ay)2
c)x2y +xy2+x2z+y2z+yz2+3xyz
d) 49.(y-4)2-9 y2-36y-36
phân tích đa thức thành nhân tử
a)70a+84b-20ab-24b2
b) x2y+xy2+x2z+xz2+y2z+yz2+3xyz
c) x2y+xy2+x2z+xz2+y2z+yz2+2xyz
a) \(70a+84b-20ab-24b^2\)
\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)
\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)
\(=\left(5a+6b\right)\left(14-4b\right)\)
\(=2\left(5a+6b\right)\left(7-2b\right)\)
b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xyz+xz^2\right)+\left(xyz+y^2z+yz^2\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)
c) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=\left(x^2y+xy^2\right)+\left(xz^2+yz^2\right)+\left(x^2z+2xyz+y^2z\right)\)
\(=xy\left(x+y\right)+z^2\left(x+y\right)+z\left(x^2+2xy+y^2\right)\)
\(=xy\left(x+y\right)+z^2\left(x+y\right)+z\left(x+y\right)^2\)
\(=\left(x+y\right)\left[xy+z^2+z\left(x+y\right)\right]\)
\(=\left(x+y\right)\left(xy+z^2+xz+yz\right)\)
\(=\left(x+y\right)\left[\left(xy+yz\right)+\left(xz+z^2\right)\right]\)
\(=\left(x+y\right)\left[y\left(x+z\right)+z\left(x+z\right)\right]\)
\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
a, 70a + 84b - 20ab - 24b2
= 14.(5a + 6b) - 4b(5a + 6b)
= (5a + 6b).(14 - 4b)
a, 70a + 84b - 20ab - 24b2
= (70a + 84b) - (20ab + 24b2)
= 14.(5a + 6b) - 4b.(5a + 6b)
= (5a + 6b).(14 - 4b)
phân tích đa thức thành nhân tử
a)70a+84b-20ab-24b2
b) x2y+xy2+x2z+xz2+y2z+yz2+3xyz
c) x2y+xy2+x2z+xz2+y2z+yz2+2xyz
a: \(70a+84b-20ab-24b^2\)
\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)
\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)
\(=\left(5a+6b\right)\left(14-4b\right)\)
\(=2\left(7-2b\right)\left(5a+6b\right)\)
b: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2\right)+\left(y^2z+yz^2\right)+3xyz\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+3xyz\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+2xyz+xyz\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z+x\right)\)
\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z+x\right)\)
\(=\left(y+z\right)\cdot x\left(x+y+z\right)+yz\left(y+z+x\right)\)
\(=\left(y+z+x\right)\cdot\left(xy+xz+yz\right)\)
c: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2+2xyz\right)+\left(y^2z+yz^2\right)\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2+2xz\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)
\(=\left(y+z\right)\left(x^2+yz+xy+xz\right)\)
\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)
phân tích đa thức thành nhân tử bằng cách nhóm hạng tử
3) x2 (x+2y) - x - 2y
4) x3 - 4x2 - 9x + 36
5) x2y + xy2 + x2z + y2z + 2xyz
3) \(x^2\left(x+2y\right)-x-2y\)
\(=x^2\left(x+2y\right)-\left(x+2y\right)\)
\(=\left(x^2-1\right)\left(x+2y\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(x+2y\right)\)
4) \(x^3-4x^2-9x+36\)
\(=\left(x^3-4x^2\right)-\left(9x-36\right)\)
\(=x^2\cdot\left(x-4\right)-9\left(x-4\right)\)
\(=\left(x-4\right)\left(x^2-9\right)\)
\(=\left(x-4\right)\left(x+3\right)\left(x-3\right)\)
\(x^2\left(x+2y\right)-x-2y\\ =x^2\left(x+2y\right)-\left(x+2y\right)\\ =\left(x^2-1\right)\left(x+2y\right)\\ =\left(x-1\right)\left(x+1\right)\left(x+2y\right)\\ ---\\ x^3-4x^2-9x+36\\ =x^2\left(x-4\right)-9\left(x-4\right)\\ =\left(x^2-9\right)\left(x-4\right)\\ =\left(x-3\right)\left(x+3\right)\left(x-4\right)\)
Phân tích đa thức thành nhân tử
x2y + xy2 + x2z + xz2 + y2z + yz2 + 3xyz
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(y^2z+yz^2+xyz\right)+\left(x^2z+xz^2+xyz\right)\)
\(=xy\left(x+y+z\right)+yz\left(y+z+x\right)+xz\left(x+z+y\right)\)
\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)
Phân tích đa thức thành nhân tử:
a) 2x-72x3
b) m3p+m2np-m2p2-mnp2
c) a(x2+4)-x(a2+4)
d) (xy+ab)2+(ay-bx)2
e) x2y-xy2+x3-y3
f) 4x4+1
Phân tích đa thức thành nhân tử:
a) 2x-72x3
b) m3p+m2np-m2p2-mnp2
c) a(x2+4)-x(a2+4)
d) (xy+ab)2+(ay-bx)2
e) x2y-xy2+x3-y3
f) 4x4+1
(Mình cần gấp ạ :3)
a) \(2x-72x^3=2x\left(1-36x^2\right)=2x\left(1-6x\right)\left(1+6x\right)\)
f) \(4x^4+1=4x^4+4x^2+1-4x^2=\left(2x^2+1\right)^2-\left(2x\right)^2=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
Bài 2:Phân tích đa thức thành nhân tử chung
a, 4(2-x)2+xy-2y
b, x(x-y)3-y(y-x)2-y2(x-y)
c, x2y-xy2-3x+3y
d, x(x+y)2-y(x+y2)+xy-x2
a) \(4\left(2-x\right)^2+xy-2y\)
\(=4\left(x-2\right)^2+\left(xy-2y\right)\)
\(=4\left(x-2\right)\left(x-2\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(4x-8\right)+y\left(x-2\right)\)
\(=\left(x-2\right)\left(4x-8+x-2\right)\)
\(=\left(x-2\right)\left(5x-10\right)\)
\(=5\left(x-2\right)^2\)
a, \(=4\left(x-2\right)^2+y\left(x-2\right)=\left(x-2\right)\left(4x-8+y\right)\)
b, \(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-xy+y^2-y^2\right]=\left(x-y\right)\left(x^3-2x^2y+xy^2-xy\right)=x\left(x-y\right)\left(x^2-2xy+y^2-y\right)\)
c, \(=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\)
d, không phân tích được
c, x2y - xy2 - 3x + 3y
= xy(x-y) - 3(x-y)
= (x-y)(x-3)
Phân tích đa thức thành nhân tử:
a) 4 ( 2 - x ) 2 + xy - 2y;
b) x ( x - y ) 3 - y ( y - x ) 2 - y 2 (x - y);
c) x 2 y - xy 2 - 3x + 3y;
d) x ( x + y ) 2 - y ( x + y ) 2 + xy - x 2
phân tích da thức sau thành nhân tử
a) x4+x3+x+1
b)x4-x3-x2+1
c)x2y+xy2-x-y
d) ax2+a2y-7x-7y
e) ax2+ay-bx2-by
g) 12x2-3xy+8xz-2yz
h) x3-x2y-x2z-xyz
mợi người giúp em nha
Bài 3: Phân tích các đa thức sau thành nhân tử bằng phương pháp nhóm các hạng tử
a) x4-x3-x+1 b)x2y+xy2-x-y
c)ax2+a2y-7x-7y d)ax2+ay-bx2-by
e)x4+x3+x+1 g)x2-2xy+y2-xz+yz
h)x2-y2-x+y i)x2-4+2x+1
giúp mình với,mình cần gấp mn ơi
a) \(=x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
\(=\left(x-1\right)^2\left(x^2+x+1\right)\)
b) \(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)
c) Đổi đề: \(a^2x+a^2y-7x-7y\)
\(=a^2\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(a^2-7\right)\)
d) \(=x^2\left(a-b\right)+y\left(a-b\right)=\left(a-b\right)\left(x^2+y\right)\)
e) \(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\left(x^2-x+1\right)\)
g) \(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
h) \(=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x+y\right)\left(x-y+1\right)\)
i) \(=\left(x+1\right)^2-4=\left(x+1-2\right)\left(x+1+2\right)=\left(x-1\right)\left(x+3\right)\)
a\(x^3\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3-1\right)\)
b)\(=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\)
d)\(=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(x^2+y\right)\left(x-b\right)\)
e)\(=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
g)\(=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
h)\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\)
i)\(=\left(x-1\right)^2-4=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\)