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x4-3x3-x+3 = (x4-3x3)-(x-3) = x3(x-3)-(x-3) = (x-3)(x3-1) = (x-3)(x-1)(x2+x+1)
3x+3y-x2-2xy-y2 = (3x+3y)-(x2+2xy+y2) = 3(x+y)-(x+y)2 = (x+y)( 3-x-y)
x2-x-12 = x(x-1)-12
3x^2−22xy−4x+8y+7y^2+1
=3x^2−21xy−3x−xy+7y^2+y−x+7y+1
=3x(x−7y−1)−y(x−7y−1)−(x−7y−1)
=(3x−y−1)(x−7y−1)
\(3x^2-22xy-4x+8y+7y^2+1\)
\(=3x^2-21xy=3x-xy+7y^2+y-x+7y+1\)
\(=3x.\left(x-7y-1\right)-y.\left(x-7y-1\right)-\left(x-7y-1\right)\)
\(=\left(3x-y-1\right)\left(x-7y-1\right)\)
~ Rất vui vì giúp đc bn ~
a) \(x^3-3x+1-3x^2=\left(x^3+1\right)-\left(3x^2+3x\right)=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)=\left(x+1\right)\left(x^2-4x+1\right)\)
b) \(2x^2+4x+2-2y^2=2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]=2\left(x+1+y\right)\left(x+1-y\right)\)
ta có : 4.x^2 -4.y^2 +4y-1=4.x^2 -(4.y^2 -4y+1)=(2x)^2 - (2y-1)^2=(2x+2y-1)(2x-2y+1)
= \(2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]=2\left(x-y+1\right)\left(x+y+1\right)\)
a) \(36-4x^2+4xy-y^2\)
\(=36-\left(2x-y\right)^2\)
\(=\left(6+2x-y\right)\left(6-2x+y\right)\)
b) \(2x^4+3x^2-5\)
\(=2x^4-2x^2+5x^2-5\)
\(=2x^2\left(x^2-1\right)+5\left(x^2-1\right)\)
\(=\left(2x^2+5\right)\left(x+1\right)\left(x-1\right)\)
Ta có : \(4x^2-3x-1\)
\(=4x^2-4x+x-1\)
\(=4x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(4x+1\right)\)
Ta có : \(x^2-7x+12\)
\(=x^2-3x-4x+12\)
\(=x\left(x-3\right)-\left(4x-12\right)\)
\(=x\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-4\right)\left(x-3\right)\)
\(3y^3+6xy^2+3x^2y=3y\left(y^2+2xy+x^2\right)=3y\left(x+y\right)^2\)
\(x^3-3x^2-4x+12=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
\(x^3+3x^2-3x-1=\left(x-1\right)\left(x^2+x+1\right)+3x\left(x-1\right)=\left(x-1\right)\left(x^2+x+1+3x\right)\)
\(=\left(x-1\right)\left(x^2+4x+1\right)\)
Tham khảo nhé~
3x^2-4x^2+2
=-x^2+2
= - ( x^2 -2 )
=\(-\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)\)