3.
a)4x^2-12xy+9y^2
b)x^4+2x^2+1
c)a^4+4-4a^2
d)-x^2-2xy-y^2
e)10a-a^2-25
g)a^4-2a^2+1
a) x^2+4x+4-y^2
b) x^2-16-4xy+4y^2
c) x^3+2x^2y +xy^2
d) 5x+5y-x^2-2xy-y^2
e) x^5-x^4+x^3-x^2
a) \(x^2+4x+4-y^2\)
\(=\left(x^2+2.x.2+2^2\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(a,=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\\ b=\left(x-2y\right)^2-16=\left(x-2y-4\right)\left(x-2y+4\right)\\ c,=x\left(x^2+2xy+y^2\right)=x\left(x+y\right)^2\\ d,=5\left(x+y\right)-\left(x+y\right)^2=\left(5-x-y\right)\left(x+y\right)\\ e,=x^4\left(x-1\right)+x^2\left(x-1\right)\\ =x^2\left(x^2+1\right)\left(x-1\right)\)
a: \(x^2+4x+4-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
b: \(x^2-4xy+4y^2-16=\left(x-2y-4\right)\left(x-2y+4\right)\)
c: \(x^3+2x^2y+xy^2=x\left(x^2+2xy+y^2\right)=x\left(x+y\right)^2\)
Phân tích đa thức thành nhân tử
a)\(4x^2-12xy+9y^2\)
b)\(x^4+2x^2+1\)
c)\(a^4+4+4a\)
d)\(-x^2-2xy-y^2\)
e)\(10a-a^2-25\)
g)\(a^2-2a^2+1\)
h)\(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(a,4x^2-12xy+9y^2\)
\(=\left(2x\right)^2-2.2x.3y+\left(3y\right)^2\)
\(=\left(2x-3y\right)^2\)
\(b,x^4+2x^2+1\)
\(=\left(x^2\right)^2+2.x^2.1+1^2\)
\(=\left(x^2+1\right)^2\)
\(c,a^4+4+4a\)
\(d,-x^2-2xy-y^2\)
\(=-\left(x^2+2xy+y^2\right)\)
\(=-\left(x+y\right)^2\)
\(e,10a-a^2-25\)
\(=-\left(a^2-10a+25\right)\)
\(=-\left(a^2-5a-5a+25\right)\)
\(=-\left[\left(a^2-5a\right)-\left(5a-25\right)\right]\)
\(=-\left[a\left(a-5\right)-5\left(a-5\right)\right]\)
\(=-a\left(a-5\right)+5\left(a-5\right)\)
\(=\left(a-5\right)\left(5-a\right)\)
\(g,a^2-2a+1\)
\(=a^2-2.a.1+1^2\)
\(=\left(a-1\right)^2\)
\(h,\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y-1\right)^2\)
C1) phân tích thành nhân tử
a) 4x^2 - 12xy + 9y^2
b) 27a^3 - 64b^3
c) (2a - 3b)(a + b )+ (5a - 2b)(3b - 2a) - (4a - 3b)^2
d) (2x - 6y)^2 - (3xy - 4)^2
C2) tìm x, biết
a) (2x - 3)^3 = (2x -9)(4x^2 +3)
b)(5x - 4) = (5x - 2)(5x + 2)
a) 4x^2 - 12xy + 9y^2
=(2x)^2 - 2.2.3xy + (3y)^2
=(2x+3y)^2
b) 27a^3 - 64b^3
=(3a)^3 - (4b)^3
=(3a - 4b) [(3a)^2 +3a.4b +(4B)^2]
d) (2x - 6y)^2 - (3xy - 4)^2
=[ (2x - 6y)+ (3xy - 4) ] [ (2x - 6y)- (3xy - 4) ]
\(1,a,4x^2-12xy+9y^2\)
\(=\left(2x\right)^2-2.3.2xy+\left(3y\right)^2\)
\(=\left(2x-3y\right)^2\)
\(b,27a^3-64b^3\)
\(=\left(3a\right)^3-\left(4b\right)^3\)
\(\left(3a-4b\right)\left(9a^2+12ab+16b^2\right)\)
Phân tích đa thức thành nhân tử - phối hợp nhiều phương pháp:
a) x^4 - 4x^3 + 4x^2.
b) 2ab^2 - a^2b - b^3
c) x^3 - 8x.
d) x^5 - x^4 + x^3 - x^2.
e) a^5 + 27a^2.
f) x^4 - 3x^3 - x + 3
g) x^3 - x^2y - x + y
Bài 2:
a) x^3 - x^2 - x + 1
b) x^4 + x^3 + x^2 - 1
c) a^2 + b^2 + 2a - 2ab
d) 4a^2 - 4b^2 - 4a + 1
e) -16x^2 + 8xy - y^2 + 49
f) x^6 - x^4 + 2x^3 + 2x ^2
g) 4x - 4y + x^2 - 2xy + y^2
Bài 3:
a) 3xy^2 - 12xy + 12x
b) (x + y)^3 - (x - y)^3
c) x^2 + 2xy + y^2 - xz - yz
d) 64xy - 96x^2y + 48x^3y - 8x^4y
e) 54x^3 + 16y^3
f) 1/2(x^2 + y^2)^2 - 2x^2y^2
g) -50 x^2y^2 + 2(x - y)^2
a) 9.(2x+3)^2 - 4.(x+1)^2
b) x^2/4 +2xy +4y^2
c) -4x^2 +12xy - 9y^2 +25
d) 25x^4 -10x^2y +y^2
GIÚP MIK DZỚI
ĐANG CẦN GẤP LẮM ẠK!!!
Phân tích đa thức thành nhân tử:
1) x2 - 4 + ( x-2)2
2) x3 - 6x2 + 9x
3) x2 -2xy + y2 -a2 + 4ab - 42
4) x4 + 4
5) 4a2(a-2b) - 10a(2b - a)
6) 3x2 - y2 + 4x -2xy +1
1) =(x+2)(x-2)+(x-2)2=(x-2)(x+2+x-2)=2x(x+2)
2)=x(x2-6x+9)=x(x-3)2
3)xem lại đề giúp mik
4)=x4+4x2-4x2+4=(x4+4x2+4)-4x2=(x2+2)2-4x2=(x2+2x+2)(x2-2x+2)
\(x^2-4+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2+x-2\right)\)
\(=2x\left(x-2\right)\)
5) \(4a^2\left(a-2b\right)-10a\left(2b-a\right)\)
\(=4a^2\left(a-2b\right)+10a\left(a-2b\right)\)
\(=\left(4a^2+10a\right)\left(a-2b\right)\)
\(=a\left(4a+10\right)\left(a-2b\right)\)
6) \(3x^2-y^2+4x-2xy+1\)
\(=\left[-\left(y-x-1\right)\right]\left(y+3x+1\right)\)
phân tích đa thức thành nhân tử
a,x^2+6xy+9y^2 4a^4-4a^2b^2+b^4 x^6+y^2-2x^3y
b,(x+y)^3-(x-y)^3 25x^4-10x^2y^2+y^4 -a^2-2a-1
c,27b^3-8a^3 x^3+9x^y+27xy^2+27y^3 16x^2-9(x+y)^2
a: \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
b: \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)
\(x^6-2x^3y+y^2=\left(x^3-y\right)^2\)
b: \(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left(x+y-x+y\right)\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\left(3x^2+y^2\right)\)
\(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)
\(-a^2-2a-1=-\left(a+1\right)^2\)
Phân tích đa thức thành nhân tử
a) (4x^2 - 3x - 18)^2 - (4x^2 + 3x)^2
b) 9(x + y - 1)^2 - 4(2x + 3y +1)^2
c) -4x^2 + 12xy - 9y^2 + 25
d) x^2 - 2xy + y^2 - 4m^2 + 4mn - n^2
a) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)
\(=\left(-6x-18\right)\left(8x^2-18\right)\)
\(=-6\left(x+3\right)\cdot2\left(4x^2-9\right)\)
\(=-12\left(x+3\right)\left(2x-3\right)\left(2x+3\right)\)
b) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=-\left(x+3y+5\right)\left(7x+9y-1\right)\)
c) Ta có: \(-4x^2+12xy-9y^2+25\)
\(=-\left(4x^2-12xy+9y^2-25\right)\)
\(=-\left[\left(2x-3y\right)^2-25\right]\)
\(=-\left(2x-3y-5\right)\left(2x-3y+5\right)\)
d) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
a) (4x2-3x-18)2-(4x2+3x)2
=(4x2-3x-18-4x2-3x)(4x2-3x-18+4x2+3x)
=(-6x-18)(8x2-18)
=-48x3+108x-144x2+324
Phân tích các đa thức sau thành nhân tử
a, ay^2 - 2ayz + az^2
b, x^2+ 6xy + 9y^2 - 16
c, 7a-7b+a^2-b^2
d, 36x^4 - 13x^2
e, 2x^3 - 18x
f, x2 - 49 + y^2 - 2xy
g, 2x+2y-x^2-xy
h, (x^2 + 3)^2 + 16
làm ơn giải chi tiết giúp mik vs ạ
a: \(=a\left(y^2-2yz+z^2\right)\)
\(=a\left(y-z\right)^2\)
b: \(=\left(x^2+6xy+9y^2\right)-16\)
=(x+3y)^2-16
=(x+3y+4)(x+3y-4)
c: \(=7\left(a-b\right)+\left(a-b\right)\left(a+b\right)\)
=(a-b)(7+a+b)
d: \(36x^4-13x^2\)
=x^2*36x^2-x^2*13
=x^2(36x^2-13)
f: x^2-2xy+y^2-49
=(x-y)^2-49
=(x-y-7)(x-y+7)
e: 2x^3-18x
=2x(x^2-9)
=2x(x-3)(x+3)
g: 2x+2y-x^2-xy
=2(x+y)-x(x+y)
=(x+y)(2-x)
h: (x^2+3)^2+16
=x^4+6x^2+25
=x^4+10x^2+25-4x^2
=(x^2+5)^2-4x^2
=(x^2-2x+5)(x^2+2x+5)