Phân tích các đa thức sau thành nhân tử
a) \(x^2-xy+x-y\)
b) \(xz+yz-5\left(x+y\right)\)
c) \(3x^2-3xy-5x+5y\)
Phân tích cá đa thức sau thành nhân tử:
a) x2 – xy + x – y; b) xz + yz – 5(x + y);
c) 3x2 – 3xy – 5x + 5y.
47 Phân tích cá đa thức sau thành nhân tử:
a) x2 – xy + x – y; b) xz + yz – 5(x + y);
c) 3x2 – 3xy – 5x + 5y.
a) x2 – xy + x – y = (x2 – xy) + (x – y)
= x(x – y) + (x -y)
= (x – y)(x + 1)
b) xz + yz – 5(x + y) = z(x + y) – 5(x + y)
= (x + y)(z – 5)
c) 3x2 – 3xy – 5x + 5y = (3x2 – 3xy) – (5x – 5y)
= 3x(x – y) -5(x – y) = (x – y)(3x – 5).
Học tốt nhé !!! Rất hân hạnh ^_^
a) x2 – xy + x – y = (x2 – xy) + (x - y)
= x(x - y) + (x -y)
= (x - y)(x + 1)
b) xz + yz – 5(x + y) = z(x + y) - 5(x + y)
= (x + y)(z - 5)
c) 3x2 – 3xy – 5x + 5y = (3x2 – 3xy) - (5x - 5y)
= 3x(x - y) -5(x - y) = (x - y)(3x - 5).
a) x2 – xy + x – y
= ( x2 – xy ) + ( x – y )
= x ( x – y ) + ( x – y )
= ( x + 1 )( x – y )
b) xz + yz – 5(x + y)
= ( xz + yz ) – 5 ( x + y )
= z ( x + y ) – 5 ( x + y )
= ( z – 5 )( x + y )
c) 3x2 – 3xy – 5x + 5y
= ( 3x2 – 3xy ) – ( 5x – 5y )
= 3x ( x – y ) – 5 ( x – y )
= ( x – y )( 3x – 5 )
Phân tích đa thức thành phân tử:
a,xz+yz-5(x+y)
b,3x^2-3xy-5x+5y
c,x^2+6x-y^2-3z^2
d,3x^2+6xy+3y^2-3z^2
a.\(xz+yz-5\left(x+y\right)\)
\(=z\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x+y\right)\left(z-5\right)\)
b.\(3x^2-3xy-5x+5y\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
c.\(x^2+6x-y^2-3z^2\)???Sai đề bài ...?
d.\(3x^2+6xy+3y^2-3z^2\)
\(=3\left(x^2+2xy+y^2-z^2\right)\)
\(=3\left[\left(x+y\right)^2-z^2\right]\)'
\(=3\left(x+y-z\right)\left(x+y+z\right)\)
Trả lời:
a, xz + yz - 5 ( x + y )
= ( xz + yz ) - 5 ( x + y )
= z ( x + y ) - 5 ( x + y )
= ( x + y ) ( z - 5 )
b, 3x2 - 3xy - 5x + 5y
= ( 3x2 - 3xy ) - ( 5x - 5y )
= 3x ( x - y ) - 5 ( x - y )
= ( x - y ) ( 3x - 5 )
c, x2 + 6x - y2 - 3z2
= - ( 3x2 - x2 + y2 - 6x )
d, 3x2 + 6xy + 3y2 - 3z2
= 3 ( x2 + 2xy + y2 - x2 )
= 3 [ ( x2 + 2xy + y2 ) - z2 ]
= 3 [ ( x + y )2 - z2 ]
= 3 ( x + y - z ) ( x + y + z )
Phân tích đa thức thành nhân tử)
a) 5x - 5y + ax - ay
b) a3 - a2x - ay + xy
c) xy ( x+ y ) + yz ( y+ z ) + xz ( x + z ) + 2xyz
a)
5x-5y+ax-ay = 5(x-y) +a(x-y) = (x-y)(5+a)
b) a^3 -a^2x-ay+xy = a^2(a-x) -y(a-x) = (a-x)(a^2-y)
c) xy(x+y) +yz(y+z) +xz(x+z) +2xyz = x^2.y+xy^2 +y^2.z+xz^2 +x^2.z+xz^2 +2xyz
= (x^2.y+x^2.z)+(xy^2+xz^2+2xyz)+(y^2.z+yz^2) = x^2(y+z) +x.(y+z)^2 +yz(y+z)
=(y+z)(x^2+x+yz)
phân tích đa thức thành nhân tử
a/ x2-xy+x-y
b/ 3x2-3xy-5x+5y
a)x2-xy+x-y
=x(x-y)+(x-y)
=(x+1)(x-y)
b)3x2-3xy-5x+5y
=3x(x-y)-5(x-y)
=(3x-5)(x-y)
a ) \(x^2-xy+x-y\).
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right).\)
b ) \(3x^2-3xy-5x+5y\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
Phân tích các đa thức sau thành nhân tử.
a, \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(z+x\right)+3xyz.\)
b, \(xy\left(x+y\right)-yz\left(y+z\right)-zx\left(z-x\right)\)
c, \(x\left(y^2-z^2\right)+y\left(z^2-x^2\right)+z\left(x^2-y^2\right)\)
a) xy(x + y) + yz(y + z) + xz(z + x) + 3xyz
= xy(X + y + z) + yz(x + y + z) + xz(X + y + z)
= (x + y +z)(xy + yz+ xz)
b) xy(x + y) - yz(y + z) - xz(z - x)
= x2y + xy2 - y2z - yz2 - xz2 + x2z
= x2(y + z) - yz(y + z) + x(y2 - z2)
= x2(y + z) - yz(y + z) + x(y + z)(y - z)
= (y + z)(x2 - yz + xy - xz)
= (y + z)[x(x + y) - z(x + y)]
= (y + z)(x + y)(x - z)
c) x(y2 - z2) + y(z2 - x2) + z(x2 - y2)
= x(y - z)(y + z) + yz2 - yx2 + x2z - y2z
= x(y - z)(y + z) - yz(y - z) - x2(y - z)
= (y - z)((xy + xz - yz - x2)
= (y - z)[x(y - x) - z(y - x)]
= (y - z)(x - z)(y -x)
phân tích đa thức thành nhân tử
a/ x2-xy+x-y
b/ 3x2-3xy-5x+5y
thank trước nha
\(x^2-xy+x-y\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-1\right)\left(x-y\right)\)
a, \(x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right).\)
\(b,3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
a/ x^2 -xy +x-y = x(x-y)+(x-y) = (x-1)(x+y)
b/ 3x^2 - 3xy -5x +5y = 3x(x-y) - 5(x-y) = (3x-5)(x-y)
Phân tích đa thức thành nhân tử
1, x\(^2\)-xy+x-y
2, xz+yz-5x-5y
3, 3x\(^2\)-3xy-5x+5y
4, x\(^2\)-2xy+y\(^2\)-xz+yz
5, 3x\(^2\)+6xy+3y\(^2\)-3z\(^2\)
6, 45+x\(^{^{ }3}\)-5x\(^2\)-9x
7, x\(^2\)-6x+5
8,x\(^2\)+7x+12
9, 2x\(^2\)-7x+3
10, 3x\(^2\)-12y\(^2\)
11, 5xy\(^2\)-10xyz+5xz\(^2\)
12,x\(^2\)-y\(^2\)-x+y
13, a\(^3\)x-ab+b-x
14, (1+x\(^2\))-4x(1-x\(^2\))
CÁC CẬU GIẢI CHI TIẾT GIÚP MÌNH VỚI Ạ
13: =x(a^3-1)-b(a-1)
=x(a-1)(a^2+a+1)-b(a-1)
=(a-1)(a^2x+a*x+x-b)
12: =(x-y)(x+y)-(x-y)
=(x-y)(x+y-1)
10: =3(x^2-4y^2)
=3(x-2y)*(x+2y)
7: =x^2-x-5x+5=(x-1)(x-5)
8: =x^2+3x+4x+12=(x+3)(x+4)
9: =2x^2-6x-x+3=(x-3)(2x-1)
phân tích đa thức thành nhân tử:
\(\left(x^2+y^2+z^2\right)\left(x+y+z\right)^2+\left(xy+yz+xz\right)^2\)
Đặt x^2+y^2+z^2 =a ; xy+yz+zx=b
=> (x+y+z)^2 =x^2+y^2+z^2+2xy+2yz+2zx =a+2b
Ta có A= (x^2+y^2+z^2)(xy+yz+zx) +(x+y+z)^2
= a(a+2b)+b^2=a^2+2ab+b^2=(a+b)^2
=(x^2+y^2+z^2 +xy+yz+zx)^2