Question

simplify: (x + y + z)² (x + y - z)²​

Answer 1

Answer:

( x + y + z)²(x + y - z)²

→ { ( x + y + z)( x + y - z) } ²

→ [ { ( x + y) + z } × { (x + y) - z} ]² [ taking ( x + y) as A and z as B , hence ( A+B)(A-B) = A²-B² ]

→ { (x + y)² - z² }²

→ { x² + 2xy + y² - z² }²

→ { ( x² + 2xy + y² ) - z²}² [ taking ( x² + 2xy + y²) as A and z² as B , hence ( A - B)² = A² - 2AB + B²]

→ ( x² + 2xy + y²)² - 2× ( x² + 2xy + y²)× z² + (z²)²

→ ( x² + 2xy + y²)² - 2z²(x² + 2xy + y²) + z⁴