Question

factorise (x+y+z)2 - (x+y-z)2

Answer 1

Expand above expression

xy^2+xz^2+yz^2+yx^2+zx^2+zy^2+2xyz

We can club terms like

xy(y+x)+yz(y+z)+zx(z+x)+xyz+xyz

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

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

=> (x+y+z)(x+z)y+xz(x+z)

=> (x+z)(y(x+y+z)+xz)

=>(x+z)(xy+y^2+yz+xz)

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

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