Question

Simplify
(x+y+z)²-(x-y-z)²​

Answer 1

(x + y + z)² - (x - y - z)²

= [(x + y + z) + (x - y - z)][(x + y + z) - (x - y - z)]

{By observation, we saw that the expression is in the form of 'a² - b²'. And, a² - b² = (a + b)(a - b).}

= (x + y + z + x - y - z)(x + y + z - x + y + z)

['+' + '-' = '-'; '+' + '+' = '+']

= (2x)(2y + 2z)

= 4xy + 4xz

∴ (x + y + z)² - (x - y - z)² = 4xy + 4xz...