Factorize the following: (x2+y2-z2)2-4x2y2.
Factorize(x2+y2-z2)2-4x2y2.
The given expression can be written as
(x2+y2-z2)2-4x2y2=(x2+y2-z2)2-2xy2
=(x2+y2-z2+2xy)(x2+y2-z2-2xy) [∴a2-b2=(a-b)(a+b)]
=(x2+y2+2xy-z2)(x2+y2-2xy-z2)
=(x+y2-z2)(x-y2-z2) [∴a+b2=a2+b2+2ab,a-b2=a2-2ab+b2]
=x+y-zx+y+zx-y-zx-y+z [∴a2-b2=(a-b)(a+b)]
=x+y-zx+y+zx-y-zx-y+z
Hence, the factored expression is (x+y-z)(x+y+z)(x-y-z)(x-y+z).
Which of the following is a factor of (x+y)3−(x3+y3)?
(a) x2+y2+2xy
(b) x2+y2−xy
(c) xy2
(d) 3xy