Phân tích nhân tử:
a)4x2yz-8xy2z+12xyz2
b)y2(a-b)+b-a
c)8m2(m-n)+10(n-m)2
d)3x(a-2b)2-(x-2)(2b-a)2
e)5a(x-y)3-(a+4)(y-x)3
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c: \(=\left(5x-y\right)\left(5x+y\right)\)
e: \(=\left(x-2\right)\left(x-3\right)\)
a) x(4y-10x)
b)3(x+2y)+(x+1)
c)(5x-y)(5x+y)
d)5x(y-z)2
e)(x-3)(x-2)
f)(2x+y)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: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
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)
a: 3x^2-12y^2
=3(x^2-4y^2)
=3(x-2y)(x+2y)
b: 5xy^2-10xyz+5xz^2
=5x(y^2-2yz+z^2)
=5x(y-z)^2
g: (a+b+c)^3-a^3-b^3-c^3
=(a+b+c-a)[(a+b+c)^2+a(a+b+c)+a^2]-(b+c)(b^2-bc+c^2)
=(b+c)[a^2+b^2+c^2+2ab+2ac+2bc+a^2+ab+ac+a^2-b^2+bc-c^2]
=(b+c)[3a^2+3ab+3bc+3ac]
=3(a+b)(b+c)(a+c)
e) Ta có: \(a^3-a^2-a+1\)
\(=a^2\left(a-1\right)-\left(a-1\right)\)
\(=\left(a-1\right)\left(a^2-1\right)\)
\(=\left(a-1\right)^2\cdot\left(a+1\right)\)
f) Ta có: \(x^3-2xy-x^2y+2y^2\)
\(=x^2\left(x-y\right)-2y\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-2y\right)\)
a) \(\left(a^2+b^2\right)^2-4a^2b^2=\left(a^2+b^2+2ab\right)\left(a^2+b^2-2ab\right)=\left(a+b\right)^2.\left(a-b\right)^2\)
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) \(-x^3+3x^2-3x+1=\left(1-x\right)^3\)
d) Đề sai ko ???
e) \(a^3-a^2-a+1=a^2\left(a-1\right)-\left(a-1\right)=\left(a-1\right)\left(a^2-1\right)=\left(a-1\right)^2\left(a+1\right)\)
f) \(x^3-2xy-x^2y+2y^2=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x-y\right)\left(x^2-2y\right)\)
a, \(=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)
b, \(\left(x+y-x+y\right)[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2]\)
\(=2y[x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2]\)
\(=2y\left(3x^2+y^2\right)\)
c,\(=3\left(x+1\right)^2\left(x^2-x+1\right)y^2\)
câu a, b áp dụng hằng đẳng thức rồi làm nha
c) 3x4y2 + 3x3y2 + 3xy2 + 3y2
= ( 3x4y2 + 3x3y2 ) + ( 3xy2 + 3y2 )
= 3x3y2 ( x + 1) + 3y2 ( x + 1 )
= ( 3x3y2 + 3y2 ) ( x + 1 )
= 3y2 ( x3 + 1 ) ( x + 1 )
= 3y2 ( x + 1 ) ( x2 - x + 1 ) ( x + 1 )
= 3y2 ( x + 1 )2 ( x2 - x + 1 )
học tốt nha
đúng gần hết nhưng bạn chưa khai triển hết, và câu cuối bạn làm không đúng:
a)=4xyz(x+(-2)y+3z)
b)=(a-b)(y-1)(y+1)
c)=2(m-n)(4m^2+5m-5m)
d)=2(a-b)^2.(x+1)
e)=2(x-y)^3.(3a+2)