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

c) x2 + 2xy + y2 – xz – yz = (x + y)2 – z(x + y) = (x + y)(x + y – z)

c) x2 + y2 + xz + yz + 2xy

= (x2 + 2xy + y2) + (xz + yz)

= (x + y)2 + z(x + y)

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

Bạn thử xem lại đề câu d nhé.

a) Ta có: \(4x\left(2x-3y\right)-8y\left(3y-2x\right)\)

\(=4x\left(2x-3y\right)+8y\left(2x-3y\right)\)

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

b) Ta có: \(4x^2-4xy+y^2-9z^2\)

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

\(=\left(2x+y+3z\right)\left(2x+y-3z\right)\)

c) Ta có: \(x^2y+yz+xy^2+xz\)

\(=xy\left(x+y\right)+z\left(x+y\right)\)

\(=\left(x+y\right)\left(xy+z\right)\)

\(1,\\ a,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\\ b,=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\\ c,=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\\ d,=x\left(x-2y\right)+t\left(x-2y\right)=\left(x+t\right)\left(x-2y\right)\\ 2,\\ \Rightarrow x^2-4x+4-x^2+9=6\\ \Rightarrow-4x=-7\Rightarrow x=\dfrac{7}{4}\\ 3,\\ a,x^2+2x+2=\left(x+1\right)^2+1\ge1>0\\ b,-x^2+4x-5=-\left(x-2\right)^2-1\le-1< 0\)