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LT
phân tích đa thức thành nhân tử
a) 4x^2+8xy-3x-6y
b)x^4y-3x^3y^2+3x^2y^3+xy^4
c)x^3-5x^2-14x
d)x^4+4y^4
1
PA
13 tháng 10 2016
\(4x^2+8xy-3x-6y=4x\left(x+2y\right)-3\left(x+2y\right)=\left(4x-3\right)\left(x+2y\right)\)
\(x^4y-3x^3y^2+3x^2y^3-xy^4=xy\left(x^3-3x^2y+3xy^2-y^3\right)=xy\left(x-y\right)^3\)
\(x^3-5x^2-14x=x\left(x^2-5x-14\right)=x\left(x^2-7x+2x-14\right)=x\left[x\left(x-7\right)+2\left(x-7\right)\right]=x\left(x-7\right)\left(x+2\right)\)
\(x^4+4y^4=\left(x^2\right)^2+2\times x^2\times2y^2+\left(2y^2\right)^2-4x^2y^2=\left(x^2+2y^2\right)^2-\left(2xy\right)^2=\left(x^2-2xy+2y^2\right)\left(x^2+2xy+2y^2\right)\)
YN
3 tháng 7 2021
\(1,\)
\(x^2-2x-4y^2-4y\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\(2,\)
\(x^4+2x^3-4x-4\)
\(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
\(3,\)
\(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)[3\left(x+y\right)-2\left(x-y\right)]\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
\(4,\)
\(x^2-y^2-2x+2y\)
\(=x^2-y^2-2x+2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
DT
1
1 tháng 12 2017
4x2+4y-4xy-3y2-1
=(4x2-4xy+y2)-(4y2-4y+1)
=(2x-y)2-(2y-1)2
=(2x-y+2y-1)(2x-y-2y+1)
=(2x+y-1)(2x-3y+1)
1 tháng 11 2021
Bài 1:
a) \(7x^2\left(x^2-5x+1\right)=7x^4-35x^3+7x^2\)
b) \(\left(2x-3\right)\left(x+7\right)=2x^2+11x-21\)
Bài 2:
a) \(4x^2y-8x^3y^2=4x^2y\left(1-2xy\right)\)
b) \(2x-4y-ax+2ay=x\left(2-a\right)-2y\left(2-a\right)=\left(2-a\right)\left(x-2y\right)\)
TL
15 tháng 6 2021
bài 1:
a) x(x-2)-5y-(x-2)=(x-5y)(x-2)
b) =(2x-3-4x)(2x-3+4x)=(-2x-3)(6x-3)
bài 2 bạn tự luyện nhé
31 tháng 7 2021
\(1,x^2-y^2+4x-4y\)
\(\left(x-y\right)\left(x+y\right)+4\left(x-y\right)\)
\(\left(x-y\right)\left(x+y+4\right)\)
\(x^2+2x-4y^2-4y\)
\(\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)\)
\(\left(x-2y\right)\left(x+2y+2\right)\)
\(3,3x^2-4y+4x-3y^2\)
\(3\left(x^2-y^2\right)-4\left(x-y\right)\)
\(3\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\)
\(\left(x-y\right)\left(3x+3y-4\right)\)
\(x^4-6x^3+54x-81\)
\(x^4+3x^3-9x^3+27x^2-27x^2+81x-27x-81\)
\(\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27x+81\right)\)
\(x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)
\(\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)
\(\left(x+3\right)\left(x-3\right)^3\)
DK
1
23 tháng 5 2022
\(x^4y-3x^3y^2+3x^2y^3+xy^4=xy\left(x^3-3x^2y+3xy^2+y^3\right)\)
QA
2 tháng 8 2021
Trả lời:
5, x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y ) ( x + 2 + y )
6, x2 + 2x - 4y2 - 4y
= ( x2 - 4y2 ) + ( 2x - 4y )
= ( x - 2y ) ( x + 2y ) + 2 ( x - 2y )
= ( x - 2y ) ( x + 2y + 2 )
7, 3x2 - 4y + 4x - 3y2
= ( 3x2 - 3y2 ) + ( 4x - 4y )
= 3 ( x2 - y2 ) + 4 ( x - y )
= 3 ( x - y ) ( x + y ) + 4 ( x - y )
= ( x - y ) [ 3 ( x + y ) + 4 ]
= ( x - y ) ( 3x + 3y + 4 )
8, x4 - 6x3 + 54x - 81
= ( x4 - 81 ) - ( 6x3 - 54x )
= ( x2 - 9 ) ( x2 + 9 ) - 6x ( x2 - 9 )
= ( x2 - 9 ) ( x2 + 9 - 6x )
= ( x - 3 ) ( x + 3 ) ( x - 3 )2
= ( x - 3 )3 ( x + 3 )
2 tháng 8 2021
a, \(x^2-y^2+4x+4=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
b, \(x^2+2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)=\left(x-2y\right)\left(x+2+2y\right)\)
c, \(3x^2-4y+4x-3y^2=3\left(x-y\right)\left(x+y\right)-4\left(y-x\right)=\left(x-y\right)\left(3x+3y+4\right)\)
d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x^2-6x+9\right)=\left(x-3\right)^3\left(x+3\right)\)
\(x^4+x^3y-4x-4y\) (sửa \(x^3\rightarrow x^4\))
\(=x^3\left(x+y\right)-4\left(x+y\right)\)
\(=\left(x+y\right)\left(x^3-4\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-4\left(x+y\right)=\)
\(=\left(x+y\right)\left(x^2-xy+y^2-4\right)\)