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\(1)x^3-2x^2+x\\ =x\left(x^2-2x+1\right)\\ =x\left(x-1\right)^2\\ 2)2x^2+4x+2-2y^2\\ =2\left(x^2+2x+1-y^2\right)\\ =2\left[\left(x+1\right)^2-y^2\right]\\ =2\left(x-y+1\right)\left(x+y+1\right)\\ 3)2xy-x^2-y^2+16\\ =16-\left(x^2-2xy+y^2\right)\\ =16-\left(x-y\right)^2=\left(x-y+4\right)\left(y-x+4\right)\\ 4)x^3+2x^2y+xy^2-9x\\ =x\left(x^2+2xy+y^2-9\right)\\ =x\left[\left(x+y\right)^2-9\right]\\ =x\left(x+y-3\right)\left(x+y+3\right)\\ 5)2x-2y-x^2+2xy-y^2\\ =\left(2x-2y\right)-\left(x^2-2xy+y^2\right)\\ =2\left(x-y\right)-\left(x-y\right)^2\\ =\left(x-y\right)\left(y-x+2\right)\)
1, x2(x2+2x+1)=x2(x+1)2
2, 2(x2+2x+1-y2)=2(x+1-y)(x+1+y)
3, 16-(x2+2xy+y2)=(4-x-y)(4+x+y)
\(x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
hk tốt
^^
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
1) Ta có: 2xy - x2 - y2 + 16
= -(x2 - 2xy + y2 - 16)
= -[(x - y)2 - 16]
= -(x - y - 4)(x - y + 4)
2) x3 + 2x2y + xy2 - 9x
= x(x2 + 2xy + y2 - 9)
= x[(x + y)2 - 9]
= x(x + y - 3)(x + y + 3)
3) x4 - 2x2 = x2(x2 - 2)
1. 2xy-x2-y2+16= -(x2-2xy+y2-16) = -(x2-2xy+y2)-16 = -(x-y)2-16= (x+y)2-42= (x+y-4).(x+y+4)
2. x3+2x2y+xy2-9x= (có sai đề không vậy?)
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)
\(a)\) \(x^2-2x-4y^2-4y\)
\(=\)\(\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\)\(\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\)\(\left(x-1-2y-1\right)\left(x-1+2y+1\right)\)
\(=\)\(\left(x-2y-2\right)\left(x+2y\right)\)
\(=\)\(2\left(x-y\right)\left(x+2y\right)\)
Chúc bạn học tốt ~
a) Ta có x2 - 2x - 4y2 - 4y
= x2 - 2x + 1 - 4y2 - 4y - 1
= (x - 1)2 - (4y2 + 4y + 1)
= (x - 1)2 - (2y + 1)2
= (x - 1 - 2y - 1)(x - 1 + 2y + 1)
= (x - 2y - 1)(x + 2y)
a, \(x^3-2x^2+x\)
\(=x^3-x^2-x^2+x\)
\(=x^2\left(x-1\right)-x\left(x-1\right)=\left(x-1\right)\left(x^2-x\right)\)
\(=x\left(x-1\right)^2\)
b, \(2x^2+4x+2-2y^2\)
\(=2x^2+2x+2x+2-2y^2\)
\(=2x\left(x+1\right)+2\left(x+1\right)-2y^2\)
\(=2\left(x+1\right)^2-2y^2\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
c, \(2xy-x^2-y^2+16\)
\(=-\left(x^2-2xy+y^2-4^2\right)\)
\(=-\left[\left(x-y\right)^2-4^2\right]=-\left(x-y-4\right)\left(x-y+4\right)\)
d, \(x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]=x\left(x+y-3\right)\left(x+y+3\right)\)
e, \(2x-2y-x^2+2xy-y^2\)
\(=-\left(x^2-2xy+y^2-2x+2y\right)\)
\(=-\left[\left(x-y\right)^2-2\left(x-y\right)\right]\)
\(=-\left(x-y\right)\left(x-y-2\right)\)
Chúc bạn học tốt!!!
cảm ơn bạn rất nhiều !!!!!!!!!!!!!