1.x^2(x-1)+16(1-x)
2.81x^2-6yz-9y^2-z^2
3.xz-yz-x^2+2xy-y^2
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\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left(\left(a-b\right)^2-\left(2c\right)^2\right)\)
\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)
x2 - y2 - 2x + 2y
= (x - y)(x + y) - 2(x - y)
= (x + y - 2)(x - y)
x+y=2=> y=2-x {cach co ban nhat}
y^2=(2-x)^2=4-4x+x^2
N=x^2+y^2=x^2+(4-4x+x^2)
N=2x^2-4x+4
N=2(x^2-2x+2)
{tach ghep BP}
\(N=2.\left[\left(x^2-2.x+1^2\right)+2-1\right]\)
\(N=2\left(x-1\right)^2+2\left(2-1\right)\)
N\(\ge\)2(2-1)=2
dang thuc xay ra khi x=1; y=1
1) \(x^2\left(x-1\right)+16\left(1-x\right)\)
\(=x^2\left(x-1\right)-16\left(x-1\right)\)
\(=\left(x^2-16\right)\left(x-1\right)\)
\(=\left(x^2-4^2\right)\left(x-1\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)
2)\(81x^2-6yz-9y^2-z^2\)
\(=81x^2-9y^2-6yz-z^2=81x^2-\left(9y^2+6yz+z^2\right)=81x^2-\left(\left(3y\right)^2+6yz+z^2\right)\)
\(=81x^2-\left(3y+z\right)^2=\left(9x\right)^2-\left(3y+z\right)^2\)
\(=\left(9x+3y+z\right)\left(9x-\left(3y+z\right)\right)=\left(9x+3y+z\right)\left(9x-3y-z\right)\)
3)\(xz-yz-x^2+2xy+y^2\)
\(=z\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=z\left(x-y\right)-\left(x-y\right)^2=\left(z+x-y\right)\left(x-y\right)\)