Question

Simplify : (x + y + z)² - (x - y + z)²​

Answer 1

Answer:

x+y+z -x+ y -z

= 2y

.....

Answer 2

Answer:

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

=(x^2+y^2+z^2+2xy+2yz+2xz)-[(x-y+z)*(x-y+z)]

=(x^2+y^2+z^2+2xy+2yz+2xz)-[x(x-y+z)-y(x-y+z)+z(x-y+z)]

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

we will take similar term together

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

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

=x^2+y^2+z^2+2xy+2yz+2xz-x^2-y^2-z^2+2xy+2yz-2xz

the opposite term will cancel

=2xy+2yz+2xy+2yz

=4xy+4yz

=4(xy+yz)