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\(-3xy^2+x^2y^2-5x^2y\)
\(=-xy\left(3y+xy-5x\right)\)
\(x\left(y-1\right)+3\left(y^3+2y+1\right)\)
\(=3y^3+6y+3+xy-x\)
Xem lại nhé ko phân tích được
\(12xy^2-12xy+3x\)
\(=3x\left(4y^2-4y+1\right)\)
\(=3x\left(2y-1\right)^2\)
\(10x^2\left(x+y\right)-5\left(2x+2y\right)y^2\)
\(=10x^2\left(x+y\right)-10\left(x+y\right)y^2\)
\(=10\left(x+y\right)\left(x-y\right)\left(x+y\right)\)
\(=10\left(x+y\right)^2\left(x-y\right)\)
\(x^4-y^4\)
\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+y^2\right)\)
\(\left(a-b\right)^3-\left(a-b\right)^3\)
\(=\left(a-b\right)^2\left(a-b-a+b\right)\)
\(\left(a^2+2ab+b^2\right)+\left(a+b\right)^3\)
\(=\left(a+b\right)^2+\left(a+b\right)^3\)
\(=\left(a+b\right)^2\left(a+b+1\right)\)
......giải ....
a. \(\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
b ...ko cần làm .. =0
c.. =(a+b)^2 +(a+b)^3=(a+b)[ (a+b)+ (a+b)^2 ]
... check mk đó .. The end•••
1) \(x^4+4=\left(x^2+2\right)^2-4x^2=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
2) \(a^4+64=\left(a^2+8\right)-16a^2=\left(a^2+4a+8\right)\left(a^2-4a+8\right)\)
3) \(x^5+x+1\)
\(=\left(x^5-x^4+x^2\right)+\left(x^4-x^3+x\right)+\left(x^3-x^2+1\right)\)
\(=x^2\left(x^3-x^2+1\right)+x\left(x^3-x^2+1\right)+\left(x^3-x^2+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
4) \(x^5+x-1\)
\(=\left(x^5+x^4-x^2\right)-\left(x^4+x^3-x\right)+\left(x^3+x^2-1\right)\)
\(=x^2\left(x^3+x^2-1\right)-x\left(x^3+x^2-1\right)+\left(x^3+x^2-1\right)\)
\(=\left(x^2-x+1\right)\left(x^3+x^2-1\right)\)
\(4\left(x^2y^2+z^2t^2+2xyzt\right)-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left[2\left(xy+zt\right)\right]^2-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2zt\right)^2-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2zt-x^2-y^2+z^2+t^2\right)\left(2xy+2zt+x^2+y^2-z^2-t^2\right)^2\)
Ta có: \(4\left(x^2y^2+2xyzt+z^2t^2\right)-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2tz\right)^2-\left(x^2+y^2-z^2-t^2\right)^2\)
\(=\left(2xy+2tz-x^2-y^2+z^2+t^2\right)\left(2xy+2tz+x^2+y^2-z^2-t^2\right)\)
\(=\left[-\left(x^2-2xy+y^2\right)+\left(z^2+2tz+t^2\right)\right]\left[\left(x^2+2xy+y^2\right)-\left(t^2-2tz+z^2\right)\right]\)
\(=\left(z+t-x+y\right)\left(z+t+x-y\right)\left(x+y-t+z\right)\left(x+y+t-z\right)\)
\(4(x^2y^2+z^2t^2+2xyzt)-(x^2+y^2-z^2-t^2)^2\)
\(=[2(xy+zt]^2-(x^2+y^2-z^2-t^2)^2\)
\(=(2xy+2zt)^2-(x^2+y^2-z^2-t^2)^2\)
\(=(2xy+2zt-x^2-y^2+z^2+t^2)(2xy+2zt+x^2+y^2-z^2-t^2)^2\)
a, = [(x-2).(x+1)]^2+(x-2)^2
= (x-2)^2.(x+1)^2+(x-2)^2
= (x-2)^2.[(x+1)^2+1]
= (x-2)^2.(x^2+2x+2)
Tk mk nha
b) \(6x^5+15x^4+20x^3+15x^2+6x+1\)
\(=6x^5+3x^4+12x^4+6x^3+14x^3+7x^2+8x^2+4x+2x+1\)
\(=\left(2x+1\right)\left(3x^4+6x^3+7x^2+4x+1\right)\)
\(=\left(2x+1\right)\left(3x^4+3x^3+3x^2+3x^3+3x^2+3x+x^2+x+1\right)\)
\(=\left(2x+1\right)\left(x^2+x+1\right)\left(3x^2+3x+1\right)\)