a, \(\left(x-z\right)^2-y^2+2y-1\)
\(=\left(x-z\right)^2-\left(y-1\right)^2\)
\(=\left(x-z-y+1\right)\left(x-z+y-1\right)\)
b, \(x^3+y^3+3y^2+3y+1\)
\(=x^3+\left(y+1\right)^3=\left(x+y+1\right)\left[x^2-x\left(y+1\right)+\left(y+1\right)^2\right]\)
\(=\left(x+y+1\right)\left(x^2-xy-x+y^2+2y+1\right)\)
c, \(1-2a+2bc+a^2-b^2-c^2\)
\(=a^2-2a+1-\left(b^2-2bc+c^2\right)\)
\(=\left(a-1\right)^2-\left(b-c\right)^2\)
\(=\left(a-1-b+c\right)\left(a-1+b-c\right)\)
d, \(x^2+3cd\left(2-3cd\right)-10xy-1+25y^2\)
\(=\left(x^2-10xy+25y^2\right)+\left[3cd\left(2-3cd\right)-1\right]\)
\(=\left(x-5y\right)^2+\left(6cd-\left(3cd\right)^2-1\right)\)
\(=\left(x-5y\right)^2-\left(3cd-1\right)^2\)
\(=\left(x-5y-3cd+1\right)\left(x-5y+3cd-1\right)\)
Chúc bạn học tốt!!!
