Phân tích đa thức sau thành nhân tử:
a,x^6+3x^5+4x^4+4x^3+4x^2+3x+1
b,x^10+x^5+1
c,(x+y+z)^3-x^3-y^3-z^3
ai lm đúng mk tick cho
Phân tích các đa thức sau thành nhân tử:
a) 3x-6
b) x2-4x+4
c) x2-y2+5x-5y
d) 8(x+y+z)3-(x+y)3-(y+z)3-(y+z)3-(z+x)3
Do câu d mình ko biết làm bởi v mình không làm được
Phân tích đa thức thành nhân tử:
a) x^3 - x^2 + 8x - 8
b) 8x^3 - 8x^2y + 2xy^2
c) (x^2 + y^2 - z^2)^2 - 4x^2y^2
d) (x^2 - y^2 - 5)^2 - 4(x^2y^2 + 4xy + 4)
e) x^3 - y^3 - 3x^2 + 3x - 1
a) (x3-x2)+(8x-8)=x(x-1)+8(x-1)=(x2+8)(x-1)
b) 8x3-8x2y+2xy2=2x(4x2-4xy+y2)
c) (x2+y2-z2)2 - 4x2y2=(x2+y2-z2)2 - (2xy)2=(x2+y2-z2-2xy)(x2+y2-z2+2xy)
Phân tích đa thức thành nhân tử:
a, \(x^3+3x^2+3x+1-27z^3\)
b, \(x^2-2xy+y^2-xz+yz\)
c, \(x^4+4x^2-5\)
a.
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)
\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)
b.
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c.
\(=x^4-1+4x^2-4\)
\(=\left(x^2-1\right)\left(x^2+1\right)+4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) Ta có: \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
b) Ta có: \(x^2-2xy+y^2-zx+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c) Ta có: \(x^4+4x^2-5\)
\(=x^4+4x^2+4-9\)
\(=\left(x^2+2\right)^2-3^2\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
Phân tích các đa thức sau thành nhân tử:
a) x^3-4x^2+4x
b) x^2-2xy+y^2-9
c)2x^3-x^2-8x+4
d) x^2-y^2-5x+5y
e) 3x^2-6xy+3y^2-12z^2
f) x^3-4x^2+4x-xy^2
g) x^3-2x^2y+xy^2-25x
h) x^3-3x+2
i) 3x^2-7x-10
\(a,=x\left(x-2\right)^2\\ b,=\left(x-y\right)^2-9=\left(x-y-3\right)\left(x-y+3\right)\\ c,=x^2\left(2x-1\right)-4\left(2x-1\right)=\left(x-2\right)\left(x+2\right)\left(2x-1\right)\\ d,=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\\ e,=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\\ f,=x\left[\left(x-2\right)^2-y^2\right]=x\left(x-y-2\right)\left(x+y-2\right)\\ g,=x\left[\left(x-y\right)^2-25\right]=x\left(x-y-5\right)\left(x-y+5\right)\\ h,=x^3-x-2x+2=x\left(x-1\right)\left(x+1\right)-2\left(x-1\right)\\ =\left(x-1\right)\left(x^2+x-2\right)=\left(x-1\right)^2\left(x+2\right)\\ i,=3x^2+3x-10x-10=\left(x+1\right)\left(3x-10\right)\)
1.Đa thức 4x(2y-z) +7y(2y-z) được phân tích thành nhân tử là :
A .(2y+z)(4x+7y)
B.(2y-z)(4x-7y)
C.(2y+z)(4x-7y)
D. (2y-z)(4x+7y)
2 Phân tích đa thức x2+3x+xy+3y thành nhân tử ta được :
A. (x+3)(y+3)
B. (x-y)(x+3)
C. (x+3)(x+y)
D. Cả 3 đều sai
Phân tích đa thức thành nhân tử
a, x^2 +6x+9-y^2
b, x^3-3x^2 -4x+12
c, 3x^2-3xy-5x+5y
d, x^3+y^3+2x^2-2xy+2y
e, x^4-2x^3+2x-1
f, x^3-4x^2+12x-27
g, xy(x+y)+yz(y+z)+xz(x+z)+2xyz
h, 8-27x^3
i, (x+y)^2-(x-y)^2
k, x^6-y^6
p/s mn giúp mk vs ạ . lm đc câu nào thì lm. ai giúp mk thì mk thấy câu tl của ng đó ở đâu mk đều tick hết
a) = (x + 3)2 - y2 = (x + 3 - y)(x + 3 + y)
b) = x2(x - 3) -4(x - 3) = (x - 3)(x2 - 4) = (x - 3)(x - 2)(x + 2)
c) = 3x(x - y) - 5(x - y) = (x - y)(3x - y)
d) Nhầm đề. tui sửa lại x3 + y3 + 2x2 - 2xy + 2y2
= x3 + y3 + 2(x2 - xy + y2) = (x + y)(x2 - xy + y2) + 2(x2 - xy + y2) = (x2 - xy + y2)(x + y + 2)
e) = x4 - x3 - x3 + x2 - x2 + x + x - 1 = x3(x - 1) - x2(x - 1) - x(x - 1) + x - 1 = (x - 1)(x3 - x2 - x + 1) = (x - 1)(x - 1)(x2 - 1) = (x - 1)3(x + 1)
f) = x3 - 3x2 - x2 + 3x + 9x - 27 = x2(x - 3) - x(x - 3) + 9(x - 3) = (x-3)(x2 - x + 9)
g) chắc là 3xyz
= x2y + xy2 + y2z + yz2 + x2z + xz2 + 3xyz = x2y + xy2 + xyz + y2z + yz2 + xyz + x2z + xz2 + xyz = (x + y + z)(xy + yz + xz)
h) = 23 -(3x)3 = (2 - 3x)(4 + 6x + 9x2)
i) = (x + y - x + y)(x + y + x - y) = 2y*2x = 4xy
k) = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy +y2)(x + y)(x2 - xy +y2).
Phân tích đa thức thành nhân tử:
a) x^2y + 2xy^2 + xy
b) x^3 + x^2 – 4x – 4
c) x^2 – 2x – 15
d) x^2 – 4 + (x – 2)^2
e) x^2 – y^2 + 2x + 1
g) (x + 9)^2 – 36x^2
h) x^2 – 2xy + y^2 – z^2 + 2zt – t^2
i) x^3 – 3x^2 + 3x – 1 – y^3
\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)
c: =(x-5)(x+3)
e: =(x+1-y)(x+1+y)
Phân tích đa thức thành nhân tử:
a) x - 2y + x^2- 4y^2
b) x^2 - 4x^2y^2 + y^2 + 2xy
c) x^6 - x^4 +2x^3 + 2x^2
d) x^3 + 3x^2 + 3x +1 - 8y^3
a) Ta có: \(x-2y+x^2-4y^2\)
\(=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x-2y\right)\left(x+2y+1\right)\)
b) Ta có: \(x^2+2xy+y^2-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
c) Ta có: \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\)
\(=x^2\left(x+1\right)\left[x^2\left(x-1\right)+2\right]\)
\(=x^2\left(x+1\right)\cdot\left(x^3-x^2+2\right)\)
d) Ta có: \(x^3+3x^2+3x+1-8y^3\)
\(=\left(x+1\right)^3-\left(2y\right)^3\)
\(=\left(x+1-2y\right)\left[\left(x+1\right)^2+2y\left(x+1\right)+4y^2\right]\)
\(=\left(x-2y+1\right)\left(x^2+2x+1+2xy+2y+4y^2\right)\)
Phân tích đa thức thành nhân tử:
a) x - 2y + x^2 - 4y^2
b) x^2 - 4x^2y^2 + y^2 + 2xy
c) x^6 - x^4 + 2x^3 + 2x^2
d) x^3 + 3x^2 + 3x + 1 - 8y^3
a, \(x-2y+x^2-4y^2=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)=\left(x-2y\right)\left(1+x+2y\right)\)
b, \(x^2-4x^2y^2+y^2+2xy=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
c, \(x^6-x^4+2x^3+2x^2=x^6+2x^3+1-x^4+2x^2-1\)
\(=\left(x^3+1\right)^2-\left(x^2-1\right)^2=\left(x^3-x^2+2\right)\left(x^3+x^2\right)\)
\(=x^2\left(x+1\right)\left(x^3-x^2+2\right)\)
d, \(x^3+3x^2+3x+1-8y^3=\left(x+1\right)^3-\left(2y\right)^3=\left(x+1-2y\right)\left(x+1+2y\right)\)
a) Ta có: \(x-2y+x^2-4y^2\)
\(=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x-2y\right)\left(1+x+2y\right)\)
b: Ta có: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)