Simplify
(x+y+z)²-(x-y-z)²
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(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...
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