Lời giải :

\(x^2-2014xy-2016xz+\left(2015^2-1\right)yz\)

\(=x^2-2014xy-2016xz+\left(2015-1\right)\left(2015+1\right)yz\)

\(=x^2-2014xy-2016xz+2014\cdot2016\cdot yz\)

\(=x\left(x-2014y\right)-2016z\left(x-2014y\right)\)

\(=\left(x-2014y\right)\left(x-2016z\right)\)

1/ \(\left(a-b\right)\left(a^2+3ab+b^2\right)+\left(a+b\right)^3+ab\left(b-a\right)=\left(a^2+2ab+b^2+ab\right)\left(a-b\right)+\left(a+b\right)^3+ab\left(b-a\right)\)= \(\left(a^2+2ab+b^2\right)\left(a-b\right)+\left(a+b\right)ab+\left(a-b\right)^3-ab\left(a-b\right)\)

= \(\left(a+b\right)^2\left(a-b\right)+\left(a+b\right)^3\)

= \(\left(a+b\right)^2\left(a-b+a+b\right)=2a\left(a+b\right)^2\)

k mình nhé!

x² - 2014xy - 2016xz + (2015² - 1)yz

= x² - 2014xy - 2016xz + (2015 - 1)(2015 + 1)yz

= x² - 2014xy - 2016xz + 2014.2016.yz

= (x² - 2014xy) - (2016xz - 2014.2016.yz)

= x(x - 2014y) - 2016z(x - 2014y)

= (x - 2014y)(x - 2016z)

#TT

x²y + xy² + x²z + xz² + y²z + yz² +3xyz

=(x²y+x²z)+(xy²+xz²)+(y²z+yz²)+3xyz

=x²(y+z)+x(y²+z²)+yz(y+z)+2xyz+xyz

=x²(y+z)+x(y²+z²+2yz)+yz(y+z+x)

=(y+z)x(x+y+z)+yz(y+x+z)

=(x+y+z)(xy+xz+yz)

x²y + xy² + x²z + xz² + y²z + yz² + 3xyz

=(x²y + xy² + xyz) + (x²z + xyz + xz²) + (xyz + y²z + yz²)

=xy(x + y + z) + xz(x + y + z) + yz(x + y +z)

=(x + y + z)(xy + xz + yz)

\(x-\sqrt{x}-2\\ =x+\sqrt{x}-2\sqrt{x}-2\\ =\sqrt{x}\left(\sqrt{x}+1\right)-2\left(\sqrt{x}+1\right)\\ =\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)

(x+5)²

\(x^2+10x+25=\left(x+5\right)^2\)

(x+5)²

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

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

\(=\left(x^4-2x^3+2x^2\right)+\left(2x^3-4x^2+4x\right)+\left(x^2-2x+2\right)\)

\(=x^2\left(x^2-2x+2\right)+2x\left(x^2-2x+2\right)+\left(x^2-2x+2\right)\)

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

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

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

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

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

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

\(=\left(x+1\right)\left(x^3-x^2+2\right)\)