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31 tháng 7 2016
a) (2x - 1)2 - (x + 3)2
= (2x - 1 - x - 3).(2x - 1 + x + 3)
= (x - 4).(3x + 2)
b) x2.(x - 3) + 12 - 4x
= x2.(x - 3) - 4x + 12
= x2.(x - 3) - 4.(x - 3)
= (x - 3).(x2 - 4)
= (x - 3).(x - 2).(x + 2)
28 tháng 9 2018
Áp dụng HĐT:
a2 - b2 = (a - b)(a + b)
\(\left(2x-1\right)^2-\left(x+3\right)^2\)
\(=\left(2x-1-x-3\right)\left(2x-1+x+3\right)\)
\(=\left(x-4\right)\left(3x+2\right)\)
23 tháng 7 2016
1/ \(x^2+x-90=\left(x^2-10x\right)+\left(9x-90\right)=x\left(x-10\right)+9\left(x-10\right)=\left(x-10\right)\left(x+9\right)\)
2/ \(2x^2+4xy+2y^2=\left(2x^2+2xy\right)+\left(2xy+2y^2\right)=2x\left(x+y\right)+2y\left(x+y\right)=\left(x+y\right)\left(2x+2y\right)\)
3/ \(2y^2-14y+24=2\left(y^2-7y+12\right)=2\left[\left(y^2-4y\right)+\left(12-3y\right)\right]=2\left[y\left(y-4\right)-3\left(y-4\right)\right]\)
\(=2\left(y-4\right)\left(y-3\right)\)
4/ \(x^8+x^4+1=\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left[\left(x^6-x^5+x^4\right)-\left(x^4-x^3+x^2\right)+\left(x^2-x+1\right)\right]\)
\(=\left(x^2+x+1\right)\left[x^4\left(x^2-x+1\right)\right]-x^2\left(x^2-x+1\right)+\left(x^2-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)\)
23 tháng 7 2016
1/ \(2x^2+3x-5=\left(2x^2+2x\right)-\left(5x+5\right)=2x\left(x+1\right)-5\left(x+1\right)=\left(x+1\right)\left(2x-5\right)\)
2/ \(16x-5x^2-3=\left(15x-5x^2\right)+\left(x-3\right)=5x\left(3-x\right)-\left(3-x\right)=\left(3-x\right)\left(5x-1\right)\)
3/ \(7x-6x^2-2=\left(3x-6x^2\right)-\left(2-4x\right)=3x\left(1-2x\right)-2\left(1-2x\right)=\left(1-2x\right)\left(3x-2\right)\)
4/ \(x^2+5x-6=\left(x^2-x\right)+\left(6x-6\right)=x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x+6\right)\)
NH
3
TM
11 tháng 7 2016
a)\(x^4-2x^3+2x-1=x^4-x^3-x^3+x+x-1\)
\(=x^3\left(x-1\right)-x\left(x^2-1\right)+\left(x-1\right)\)
\(=x^3\left(x-1\right)-x\left(x-1\right)\left(x+1\right)+\left(x-1\right)\)
\(=x^3\left(x-1\right)-\left(x^2+x\right)\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left[x^3-\left(x^2+x\right)+1\right]\)
\(=\left(x-1\right)\left(x^3-x^2-x+1\right)\)
\(=\left(x-1\right)\left[x^2\left(x-1\right)-\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x-1\right)\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)^3\left(x+1\right)\)
b)\(x^4+2x^3+2x^2+2x+1=x^4+x^3+x^3+x^2+x^2+x+x+1\)
\(=x^3\left(x+1\right)+x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+x^2+x+1\right)\)
\(=\left(x+1\right)\left[x^2\left(x+1\right)+\left(x+1\right)\right]\)
\(=\left(x+1\right)\left(x+1\right)\left(x^2+1\right)\)
\(=\left(x+1\right)^2\left(x^2+1\right)\)
TH
2
2T
14 tháng 8 2019
\(x^4+2x^3-4x-4\)
\(=x^4+2x^3-4x-4+2x^2-2x^2\)
\(=\left(x^4-2x^2\right)+\left(2x^3-4x\right)+\left(2x^2-4\right)\)
\(=x^2\left(x^2-2\right)+2x\left(x^2-2\right)+2\left(x^2-2\right)\)
\(=\left(x^2+2x+2\right)\left(x^2-2\right)\)
\(=\left(x^2+2x+2\right)\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
2T
14 tháng 8 2019
\(x^4-2x^3+2x-1\)
\(=\left(x^4-3x^3+3x^2-x\right)+\left(x^3-3x^2+3x-1\right)\)
\(=x\left(x-1\right)^3+\left(x-1\right)^3\)
\(=\left(x+1\right)\left(x-1\right)^3\)
22 tháng 6 2016
x4 + 2x3 + 2x2 + 2x + 1
= x4 - 2x2 =
= x2 x x2 - x2 - x2 + 1 = x2 (1- x2 ) + ( 1 - x2 )
= ( 1 - x2 ) x ( 1 - x2 )
= ( 1 - x2 ) 2
22 tháng 6 2016
- SKT_Twisted Fate Âm Phủ
- Sai rồi :
- \(x^4-2x^2=?\)
TN
1
MN
2 tháng 2 2020
Ta có :
\(x^6+3x^5-2x^4+7x^3-2x^2+3x+1\)
\(=x^6-x^5+x^4+4x^5-4x^4+4x^3+x^4-x^3+x^2+4x^3-4x^2+4x+x^2-x+1\)
\(=x^4\left(x^2-x+1\right)+4x^3\left(x^2-x+1\right)+x^2\left(x^2-x+1\right)+4x\left(x^2-x+1\right)+\left(x^2-x+1\right)\)
\(=\left(x^2-x+1\right)\left(x^4+4x^3+x^2+4x+1\right)\)
TN
23 tháng 6 2016
x4-2x3+2x-1
=x4-3x3+3x2-x+x3-3x2+3x-1
=x(x3-3x2+3x-1)+1(x3-3x2+3x-1)
=(x3-3x2+3x-1)(x+1)
=(x-1)3(x+1)
x4-2x3+2x-1
=(x4-1)+(-2x3+2x)
=(x2+1)(x2-1)-2x(x2-1)
=(x2-1)(x2+1-2x)
=(x-1)(x+1)(x-1)2
=(x-1)3(x+1)