(x+2y)²-x²-2xy(a+b)²-4(a-b)²x^3n+y^3n x^6+24x^3+144x²-y²-z²+2yz+x+y+zm²+n+2m+2n+2mn+1

(x+2y)²-x²-2xy(a+b)²-4(a-b)²x^3n+y^3n x^6+24x^3+144x²-y²-z²+2yz+x+y+zm²+n+2m+2n+2mn+1
(x+2y)²-x²-2xy
(a+b)²-4(a-b)²
x^3n+y^3n
x^6+24x^3+144
x²-y²-z²+2yz+x+y+z
m²+n+2m+2n+2mn+1

(x+2y)²-x²-2xy(a+b)²-4(a-b)²x^3n+y^3n x^6+24x^3+144x²-y²-z²+2yz+x+y+zm²+n+2m+2n+2mn+1
1.(x+2y)^2-x^2-2xy =(x+2y)^2-(x^2+2xy) =(x+2y)^2-x(x+2y) =(x+2y)[(x+2y)-x] =2y(x+2y) 2.(a+b)^2-4(a-b)^2 =[(a+b)-2(a-b)][(a+b)+2(a-b)] =(a+b-2a+2b)(a+b+2a-2b) =(-a+3b)(3a-b) =-(a-3b)(3a-b) 3.x^3n+y^3n =n(x^3+y^3) =n(x+y)(x^2+y^2-xy) 4.x^6+24x^3+144=(x^3+12)^2 5.x^2-y^2-z^2+2yz+x+y+z =x^2-(y^2+z^2-2yz)+(x+y+z) =x^2-(y-z)^2+(x+y+z) =[x-(y-z)][x+(y-z)]+(x+y+z) =(x-y+z)(x+y-z)+(x+y+z) 6.m^2+n^2+2m+2n+2mn+1 =(m^2+2mn+n^2)+(2m+2n)+1 =(m+n)^2+2(m+n)+1 =[(m+n)+1]^2 =(m+n+1)^2