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1: =z(x-y)-5(x-y)=(x-y)(z-5)
2: \(=x^2\left(1-x\right)-xy\left(1-x\right)\)
\(=x\left(1-x\right)\left(x-y\right)\)
3: \(=4x^2-\left(t^2+4ty+4y^2\right)\)
\(=\left(2x\right)^2-\left(t+2y\right)^2\)
\(=\left(2x-t-2y\right)\left(2x+t+2y\right)\)
4: \(=-\left(x^2-4x+4-y^2\right)\)
\(=-\left(x-2-y\right)\left(x-2+y\right)\)
a) \(2x+2y\)
\(=2\left(x+y\right)\)
b) \(5x+20y\)
\(=5\left(x+4y\right)\)
c) \(6xy-30y\)
\(=6y\left(x-5\right)\)
d) \(5x\left[x-110-10y\left(x-11\right)\right]\)
\(=5x\left(x-110-10xy+110\right)\)
\(=5x\left(x-10xy\right)\)
\(=5x^2\left(1-10y\right)\)
e) \(x^3-4x^2+x\)
\(=x\left(x^2-4x+1\right)\)
f) \(x\left(x+y\right)-\left(2x+2y\right)\)
\(=x\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-2\right)\)
h) \(5x\left(x-2y\right)+2\left(2y-x\right)\)
\(=5x\left(x-2y\right)-2\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x-2\right)\)
i) \(x^2y^3-\dfrac{1}{2}x^4y^8\)
\(=x^2y^3\left(1-\dfrac{1}{2}xy^5\right)\)
j) \(a^2b^4+a^3b-abc\)
\(=ab\left(ab^3+a^2-c\right)\)
\(x^2+2xy+7x+7y+y^2+10\)
\(=\left(x^2+2xy+y^2\right)+\left(7x+7y\right)+\frac{49}{4}-\frac{9}{4}\)
\(=\left(x+y\right)^2+7\left(x+y\right)+\frac{49}{4}-\frac{9}{4}\)
\(=\left(x+y+\frac{7}{2}\right)^2-\frac{9}{4}\)
\(=\left(x+y+\frac{7}{2}-\frac{3}{2}\right)\left(x+y+\frac{7}{2}+\frac{3}{2}\right)\)
\(=\left(x+y+2\right)\left(x+y+5\right)\)
b)Ta có: x2y+xy2+x+y=2010
<=>xy.x+xy.y+x+y=2010
<=>11x+11y+x+y=2010
<=>12(x+y)=2010
<=>x+y=167,5
=>(x+y)2=28056,25
<=>x2+y2+2xy=28056,25
<=>x2+y2=28034,25
Bài nhiều quá... nhìn mik nổi gai ốc lun...oh my god sao mà nhiều vậy nè .
Mik định giải giúp bạn nhưng bây h mik hoảng quá ... nhiều vậy chắc mik chết mất... ToT ... >.< =)))
a) \(x^2-3x+xy-3y\)
\(=x\left(x-3\right)+y\left(x-3\right)\)
\(=\left(x+y\right)\left(x-3\right)\)
b) \(x^2+y^2-2xy-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y+5\right)\left(x+y-5\right)\)
c) \(4x^2-4xy+y^2=\left(2x-y\right)^2\)
m) \(81-x^2+2xy-y^2\)
\(=9^2-\left(x-y\right)^2\)
\(=\left(9-x+y\right)\left(9+x-y\right)\)
k) \(x^2-xy-x+y\)
\(=x\left(x-y\right)-\left(x-y\right)\)
\(=\left(x-1\right)\left(x-y\right)\)
1. \(x^3-x^2+x-1=(x^3-x^2)+(x-1)\)
\(=x^2(x-1)+(x-1)=(x^2+1)(x-1)\)
2. \(6x^2y-2xy^2+3x-y=2xy(3x-y)+(3x-y)\)
\(=(3x-y)(2xy+1)\)
3. \(4x^2+1\) thì còn cái gì để phân tích hả bạn? Hay ý bạn là \(4x^4+1\)?
\(4x^4+1=(2x^2)^2+1=(2x^2)^2+1+4x^2-4x^2\)
\(=(2x^2+1)^2-(2x)^2=(2x^2+1-2x)(2x^2+1+2x)\)
4. \(x^2-9x+8=(x^2-x)-(8x-8)\)
\(=x(x-1)-8(x-1)=(x-1)(x-8)\)
5. \(x^3-2x^2y+3xy^2=x(x^2-2xy+3y^2)\)
6. \(x^2-6x+y-y^2\) (sai đề)
7. \(x^2-xy-2x+2y=(x^2-xy)-(2x-2y)\)
\(=x(x-y)-2(x-y)=(x-y)(x-2)\)
x3-4x2+12x-27
=(x3-27)+(-4x2+12x)
=(x-3)(x2+3x+9)-4x.(x-3)
=(x-3)(x2+3x+9-4x)
=(x-3)(x2-x+9)
x2+y2-x2y2+xy-x-y
=x2-x+y2-x2y2+xy-y
=x.(x-1)-y2.(x2-1)+y.(x-1)
=x.(x-1)-y2.(x-1)(x+1)+y.(x-1)
=(x-1)[x-y2.(x+1)+y]
=(x-1)(x-xy2-y2+y)
=(x-1)[-x.(y2-1)-y.(y-1)]
=(x-1)[-x.(y-1)(y+1)-y.(y-1)]
=(x-1)(y-1)[-x.(y+1)-y]
=(x-1)(y-1)(-xy-x-y)