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\(x^2+6x-y^2+9\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
c) 2x^3y - 2xy^3 - 4xy^2 - 2xy
= 2xy ( x^2 - y^2 - 2y - 1 )
= 2xy ( x^2 - ( y^2 + 2y + 1 )
= 2xy ( x^2 - ( y + 1 )^2 )
= 2x ( x - y - 1 )( x + y + 1 )
sai bạn ơi !
đáp án là
= 2xy (x + y + 1) (x - y + 1)
that pun cho ban Nguyen Dieu Thao :((
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
Sửa đề :
\(x^3+y^3+2x^2+2xy\)
\(=\left(x^3+y^3\right)+\left(2x^2+2xy\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+2x\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+2x\right)\)
\(x^2+y^2-2x-2y+2xy-3\)
\(=x^2+y^2+1-2x-2y+2xy-4\)
\(=\left(x+y-1\right)^2-2^2\)
\(=\left(x+y-3\right).\left(x+y+1\right)\)
1)\(=x^2\left(x-y\right)-y\left(x-y\right)\\ =\left(x-y\right)\left(x^2-y\right)\)
2)\(=\left(x^2+x\right)-\left(2xy+2y\right)\\ =x\left(x+1\right)-2y\left(x+1\right)\\ =\left(x+1\right)\left(x-2y\right)\)
3)\(=\left(x^2+2.x.2y+4y^2\right)-y^2\\ =\left(x+2y\right)^2-y^2\\ =\left(x+2y+y\right)\left(x+2y-y\right)\)
1) x3 - x2y - xy + y2
= (x3 - x2y) - (xy - y2)
= x2.(x - y) - y.(x - y)
= (x - y).(x2 - y)
2) x2 - 2xy + x - 2y
= (x2 + x) - (2xy + 2y)
= x.(x + 1) - 2y.(x + 1)
= (x + 1).(x - 2y)
3) x2 + 4xy + 3y2
= x2 + 3xy + xy + 3y2
= (x2 + 3xy) + (xy + 3y2)
= x.(x + 3y) + y.(x + 3y)
= (x + 3y).(x + y)
1 ) \(x^3-x^2y-xy+y^2\)
\(=\left(x^3-x^2y\right)-\left(xy-y^2\right)\)
\(=x^2.\left(x-y\right)-y.\left(x-y\right)\)
\(=\left(x-y\right).\left(x^2-y\right)\)
2 ) \(x^2-2xy+x-2y\)
\(=\left(x^2+x\right)-\left(2xy+2y\right)\)
\(=x.\left(x+1\right)-2y.\left(x+1\right)\)
\(=\left(x+1\right).\left(x-2y\right)\)
3 ) \(x^2+4xy+3y^2\)
\(=x^2+3xy+xy+3y^2\)
\(=\left(x^2+3xy\right)+\left(xy+3y^2\right)\)
\(=x.\left(x+3y\right)+y.\left(x+3y\right)\)
\(=\left(x+3y\right).\left(x+y\right)\)
Bài 1:
a) 2x^2 -3x + 1 = 2x^2 -2x -x +1 = 2x.(x-1) - (x-1) = (x-1).(2x-1)
b) 2x^3y - 2xy^3 - 4xy^2 - 2xy = 2xy.(x^2 - y^2 - 2y -1) = 2xy.[ x^2 - (y^2 + 2y+1)] = 2xy.[x^2 - (y+1)^2]
= 2xy.(x-y-1).(x+y+1)
c) (x^2 + x+3).(x^2 + x +5) - 8 = (x^2+x+4-1).(x^2+x+4+1) - 8 = (x^2+x+4)^2 - 1 - 8 = (x^2+x+4)^2 - 3^2
= (x^2+x+4-3).(x^2+x+4+3) = (x^2+x+1).(x^2+x+7)
Bài 2:
a) (x+2).(x^2-2x+4) - (x^3+2x) = 0
x^3 + 8 - x^3 - 2x = 0
8 - 2x = 0
x = 4
b) x^2 - 2x - 8 = 0
x^2 +2x - 4x - 8 = 0
x.(x+2) - 4.(x+2) = 0
(x+2).(x-4) = 0
...
bn tự làm tiếp nha
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
\(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)