\(2x^3y-2xy^3-4xy^2-2xy\)

\(=2xy.\left(x^2-y^2-2y-1\right)\)

\(=2xy.[x^2-\left(y^2+2y+1\right)]\)

\(=2xy.[x^2-\left(y+1\right)^2]\)

\(=2xy.\left(x+y+1\right).\left(x-y-1\right)\)

Vậy chọn đáp án A

chọn A

\(x^3-x=6\)

\(\Rightarrow x.\left(x^2-1\right)=6\)

\(\Rightarrow x.\left(x-1\right).\left(x+1\right)=6\)

\(x^6-2x^4+x^3+x^2-x\)

\(=x^6-x^5+x^5-x^4-x^4+x^3+x^2-x\)

\(=x^5.\left(x-1\right)+x^4.\left(x-1\right)-x^3.\left(x-1\right)+x.\left(x-1\right)\)

\(=\left(x-1\right).\left(x^5+x^4-x^3+x\right)\)

\(=\left(x-1\right).[x^4.\left(x+1\right)-x.\left(x^2-1\right)]\)

\(=\left(x-1\right).\left(x+1\right).[x^4-x.\left(x-1\right)]\)

\(=\left(x-1\right).\left(x+1\right).\left(x^4-x^2+x\right)\)

\(=x.\left(x-1\right).\left(x+1\right).\left(x^3-x+1\right)\)

\(=6.\left(6+1\right)\)

\(=42\)

Vậy giá trị của biểu thức \(B=42\)khi \(x^3-x=6\)

1)2xy−2y²+3x−3y1)2xy−2y²+3x−3y

=2y(x−y)+3(x−y)=2y(x−y)+3(x−y)
=(2y+3)(x−y)=(2y+3)(x−y)

2)x²−9y²+x+3y2)x²−9y²+x+3y

=x²−(3y)²+(x+3y)=x²−(3y)²+(x+3y)

=(x−3y)(x+3y)+(x+3y)=(x−3y)(x+3y)+(x+3y)

=(x−3y+1)(x+3y)=(x−3y+1)(x+3y)
3)3x(2x−3)−6x+93)3x(2x−3)−6x+9
=3x(2x−3)−3(2x−3)=3x(2x−3)−3(2x−3)
=(3x−3)(2x−3)=(3x−3)(2x−3)
=3(x−1)(2x−3)=3(x−1)(2x−3)

4)y²−25−x²−10x4)y²−25−x²−10x
=−(x²+10x+25)+y²=−(x²+10x+25)+y²
=−(x+5)²+y²=−(x+5)²+y²

=y²−(x+5)²=y²−(x+5)²
=(y−x−5)(y+x+5)=(y−x−5)(y+x+5)
5)x²−10x+245)x²−10x+24

=x²−4x−6x+24=x²−4x−6x+24
=x(x−4)−6(x−4)=x(x−4)−6(x−4)
=(x−6)(x−4)

=[(x+2)(x+5)][(x+3)(x+4)]−24=(x2+7x+10)(x2+7x+12)−24=(x2+7x+11)2−1−24=(x2+7x+11)2−25=(x2+7x+11−5)(x2+7x+11+5)=(x2+7x+6)(x2+7x+16)=(x+1)(x+6)(x2+7x+16)

= ( x -3y)( x+3y) - 4( x -3y)

= (x -3y)(x + 3y -4)

x(x-4)=0

suy ra x=0:X=4

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