phân tíchthành nhân tử
a/x^3+3x^2+6x+4
b/3a^2c^2+bd+3abc+acd
c/3a^2-6ab+3b^2-12c^2
d/x^2+y^2-x^2y^2+xy-x-y
e/a^6-b^6
phân tíchthành nhân tử
a/x^3+3x^2+6x+4
b/3a^2c^2+bd+3abc+acd
c/3a^2-6ab+3b^2-12c^2
d/x^2+y^2-x^2y^2+xy-x-y
e/a^6-b^6
a ) \(x^3+3x^2+6x+4\)
\(=x^3+3x^2+3x+1+3x+3\)
\(=\left(x+1\right)^3+3\left(x+1\right)\)
\(=\left(x+1\right)\left[\left(x+1\right)^2+3\right]\)
\(=\left(x+1\right)\left(x^2+2x+4\right)\)
b ) \(3a^2c^2+bd+3abc+acd\)
\(=\left(3a^2c^2+3abc\right)+\left(bd+acd\right)\)
\(=3ac\left(ac+b\right)+d\left(ac+b\right)\)
\(=\left(3ac+d\right)\left(ac+b\right)\)
c ) \(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2\right)-3\left(2c\right)^2\)
\(=3\left[a^2-2ab+b^2-\left(2c\right)^2\right]\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)
d ) \(x^2+y^2-x^2y^2+xy-x-y\)
\(=-x^2y^2+x^2+y^2-y+xy-x\)
\(=-x^2\left(y^2-1\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=-x^2\left(y+1\right)\left(y-1\right)+\left(x+y\right)\left(y-1\right)\)
\(=\left(y-1\right)\left[-x^2\left(y+1\right)+x+y\right]\)
\(=\left(y-1\right)\left[-x^2y-x^2+x+y\right]\)
\(=\left(y-1\right)\left[x\left(1-x\right)+y\left(1-x^2\right)\right]\)
\(=\left(y-1\right)\left[x\left(1-x\right)+y\left(1+x\right)\left(1-x\right)\right]\)
\(=\left(y-1\right)\left[x+y\left(1+x\right)\right]\left(1-x\right)\)
e ) \(a^6-b^6=\left(a^3\right)^2-\left(b^3\right)^2=\left(a^3-b^3\right)\left(a^3+b^3\right)\) \(=\left(a-b\right)\left(a^2+ab+b^2\right)\left(a+b\right)\left(a^2-ab+b^2\right)\)
a, \(x^3+3x^2+6x+4\)
\(=\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(4x+4\right)\)
\(=x^2\left(x+1\right)+2x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+2x+4\right)\)
e, \(a^6-b^6\)
\(=\left(a^3\right)^2-\left(b^3\right)^2\)
\(=\left(a^3-b^3\right)\left(a^3+b^3\right)\)
Phân tích đa thức thành nhân tử
A, 3a^2c^2+bd+3abc+acd
B, a^2c-a^2.d-b^2.d+b^2.c
C, 8x^2+4xy-2ax-ay
D, x^2-y^2-2xy-y^2
E, 3a^2-6ab+3b^2-12c^2
Giup mk nha do j mk can on trc :3
\(A=3a^2c^2+bd+3abc+acd=\left(3a^2c^2+3abc\right)+\left(bd+acd\right)=3ac\left(ac+b\right)+d\left(b+ac\right)\\ =\left(3ac+d\right)\left(ac+b\right)\)
\(B=a^2c-a^2d-b^2d+b^2c=a^2\left(c-d\right)-b^2\left(c-d\right)=\left(a^2-b^2\right)\left(c-d\right)\\=\left(a-b\right)\left(a+b\right)\left(c-d\right)\)
\(C=8x^2+4xy-2ax-ay=\left(8x^2+4xy\right)-\left(2ax+ay\right)=4x\left(2x+y\right)-a\left(2x+y\right)\\ =\left(4x-a\right)\left(2x+y\right)\)
\(E=3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2\right)-12c^2=3\left(a-b\right)^2-12c^2\\ =3\left[\left(a-b\right)^2-4c^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)
Phân tích đa thức thành nhân tử
A, 3a^2c^2+bd+3abc+acd
B, a^2.c-a^2.d-b^2.d+b^2.c
C, 8x^2-4xy-2ax-ay
D, x^2-y^2-2yz-y^2
E, 3a^2-6ab+3b^2-12c^2
F, x^3-2xy+y^2-m^2+2mn-n^2
G, x^4-x^3y-x+y
H, x^3-4x^2+8x+8
Giup mk nha you do hoc roi
Bài 1: Phân tích đa thức sau :
a)2x(xy+y^2-3)
b)(x-y)(2x+y)
c)(x-2y)^2
d)(2x-y)(y+2x)
bài 2: Phân tích các đơn thức thành nhân tử
a)3x^2-3xy
b)x^2-4y^2
c)3x-3y+xy-y^2
d)x^2-1+2y-y^2
Bài 3: Tìm x biết:
a)3x^2-6x=0
b)Tìm x,y thuộc z biết: x^2+4y^2-2xy=4
Bài 2:
a: \(3x^2-3xy=3x\left(x-y\right)\)
b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)
d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)
Phân tích các đa thức sau thành nhân tử:
1) x^2 - y^2 - 2x + 2y
2) 2x + 2y - x^2 - xy
3) 3a^2 - 6ab + 3b^2 - 12c^2
4) x^2 - 25 + y^2 +2xy
5) a^2 + 2ab +b^2-ac-bc
6) x^2 - 2x - 4y^2 - 4y
7) x^2y - x^3 - 9y + 9x
8) x^2(x+1) + 16(1-x)
1)
x2-y2-2x+2y
=(x-y)(x+y)-2(x-y)
=(x-y)(x+y-2)
2)
2x+2y-x2-xy
=2(x+y)-x(x+y)
=(2-x)(x+y)
3)
3a2-6ab+3b2-12c2
=3(a2-2ab+b2)-3(4c2)
=3(a-b)2-3(4c2)
=3[(a-b)2-4c2 ]
=3(a-b-2c)(a-b+2c)
4)
x2-25+y2+2xy
=(x+y)2-25
=(x+y-5)(x+y+5)
1) x^2 - y^2 - 2x + 2y= ( x^2 - y^2) - ( 2x + 2y) = (x-y -2 ) (x+y)
2) 2x + 2y - x^2 - xy = 2 (x+y) - x(x+y) = (2-x)(x+y)
4) x^2 - 25 + y^2 +2xy = x^2 + 2xy + y^2 - 25 = (x+y)^2 - 5^2 = (x+y-5)(x+y+5)
5) a^2 + 2ab +b^2-ac-bc= (a+b)^2- ac + bc = (a+b)^2 - c(a+b) = (a+b)(a+b-c)
6) x^2 - 2x - 4y^2 - 4y = (x^2 - 4y^2) - (2x+4y) = (x - 2y)(x+2y) - 2 (x+2y) = (x-2y-2)(x+2y)
7) x^2y - x^3 - 9y + 9x = x^2 (y-x) - 9(y-x) = (x^2 - 9)(y-x)= (x^2 - 3^2)(y-x) = (x-3)(x+3)(y-x)
- Xl câu 3 , 8 t hk biết lm
phân tích đa thức thành nhân tử
a, x^2-y^2-2x+2y
b, 2x+2y-x^2-xy
c, 3a^2-6ab+3b^2-12c^2
d,x^2-25+y^2-2xy
e, a^2+2ab+b^2-ac-bc
f,x^2-2x-4y^2-4y
g,x^2y-x^3-9y+9x
h,x^2(x-1)+16(1-x)
\(a,x^2-y^2-2x+2y=\left(x^2-y^2\right)-\left(2x-2y\right)=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right).\) \(b,2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(x+y\right)\left(2-x\right)\)
\(c,3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3.\left(\left(a-b\right)^2-\left(2c\right)^2\right)\)
\(=3\left(a-b-2c\right).\left(a-b+2c\right)\)
\(d,x^2-25+y^2-2xy=\left(x^2-2xy+y^2\right)-5^2=\left(x-y\right)^2-5^2\)
\(=\left(x-y+5\right)\left(x-y-5\right)\)
\(e,a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)
\(f,x^2-2x-4y^2-4y=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\(h,x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
1.phân tích đa thức thành nhân tử
x^4+3x^3-9x-9
x^2+6x-y^2+9
x^2+y^2-z^2-9t^2-2xy+6zt
7x^2-7xy-4x+4y
x^4+3x^3-9x-27
3a^2-6ab+3b^2-12c^2
x^2+3cs(2-3cd)-10xy-1+25y^2
Phân tích đa thức sau thành nhân tử :
\(a,x^2-y^2-2x+2y\)
\(b,3a^2-6ab+3b^2-12c^2\)
\(c,x^2-25+y^2+2xy\)
a)\(x^2-y^2-2x+2y=\left(x^2-2x+1\right)-\left(y^2-2y+1\right)\)
\(=\left(x-1\right)^2-\left(y-1\right)^2=\left(x-1+y-1\right)\left(x-1-y+1\right)\)
\(=\left(x+y-2\right)\left(x-y\right)\)
b)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)\)\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)
Phan tich da thuc thanh nhan tu
a) x^2 - 7xy + 10y^2
b) 4x^2 + 12x - 27
c) 81x^4 + 4
d) 3a^2 - 6ab + 3b^2 - 12c^2
e) x^3 + 6x^2 +11x +6