\(a,\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\\ =\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\\ =\left(a-b\right).\left[\left(a+2b\right)+\left(2a-b\right)-\left(a+3b\right)\right]\\ =\left(a-b\right).2a\\ b,5xy^3-2xyz-15y^2+6z\\ =5y^2\left(xy-3\right)-2z\left(xy-3\right)\\ =\left(5y^2-2z\right)\left(xy-3\right)\)
\(c,\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)-\left(y-2x\right)\\ =\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)+\left(2x-y\right)\\ =\left(2x-y\right).\left(x+y+3x-y+1\right)\\ =\left(2x-y\right).\left(4x+1\right)\\ d,ab^3c^2-a^2b^2c^2+ab^2c^3-a^2bc^3\\ =abc.\left(b^2c-abc+bc^2-ac^2\right)\)
c: =(2x-y)(x+y+3x-y+1)
=(2x-y)(4x+1)
d: =abc^2(b^2-ab+bc-ac)
=abc^2*[b(a-b)+c(b-a)]
=abc^2*(a-b)(b-c)
e: =(y-z)(x^2-y^2)+z^2(x-y)
=(y-z)(x-y)(x+y)+z^2(x-y)
=(x-y)[(y-z)(x+y)+z^2]
=(x-y)(xz-y^2-xz-yz+z^2]
