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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
\(-3x^2+4x-2020\)
\(=-3\left(x^2-\frac{4}{3}x+\frac{2020}{3}\right)\)
\(=-3\left(x^2-\frac{4}{3}x+\frac{4}{9}+\frac{6056}{9}\right)\)
\(=-3\left[\left(x-\frac{2}{3}\right)^2+\frac{6056}{9}\right]\)
\(=-3\left(x-\frac{2}{3}\right)^2-\frac{6056}{3}\ge-\frac{6056}{3}\)
(Dấu "=" \(\Leftrightarrow x-\frac{2}{3}=0\Leftrightarrow x=\frac{2}{3}\))
\(3x^2+4x-7\)
\(=3x^2-3x+7x-7\)
\(=\left(3x^2-3x\right)+\left(7x-7\right)\)
\(=3x\left(x-1\right)+7\left(x-1\right)\)
\(=\left(3x+7\right)\left(x-1\right)\)
\(3x^2+4x-7\)
\(=3x^2-3x+7x-7\)
\(=\left(3x^2-3x\right)+\left(7x-7\right)\)
\(=3x\times\left(x-1\right)+7\times\left(x-1\right)\)
\(=\left(3x+7\right)\times\left(x-1\right)\)
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 ~
= \(2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]=2\left(x-y+1\right)\left(x+y+1\right)\)
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
\(3x-4x^2+7=-\left(4x^2-3x-7\right)=-\left(x+1\right)\left(4x-7\right)\)
3x-4x2+7
=-4x2+3x+7
=-4x2-4x+7x+7
=-(4x2+4x)+(7x+7)
=-4x(x+1)+7(x+1)
=(x+1)(-4x+7)
gợi ý thui, làm mêt lắm
4x2 - 1 = (2x)2 - 12
1- 2x = -(2x-1)
\(3x^2+4x+x^2-4\\ =4x^2+4x-4\\ =4\left(x^2+x-1\right)\)
3x^2-4x^2+2
=-x^2+2
= - ( x^2 -2 )
=\(-\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)\)