Question

using identies find the product of (x-y) ^4and(x+y)^4

Answer 1

We use the identities:
  
   (x+y) (x-y)  = x² - y²
   (x + y)²  = x² + y² + 2xy
   (x + y + z)² = x² + y² + z² + 2 xy + 2 yz + 2 zx
   ( x y )ⁿ = xⁿ yⁿ
    xᵇ xᵃ  = x⁽ᵃ⁺ᵇ⁾


(x-y)⁴ (x+y)⁴
  = [(x-y) (x+y)]⁴ = (x² - y²)⁴
  = [(x² - y²)² ]²
   = [x⁴ + y⁴ - 2 x² y²] ²
   = x⁸ + y⁸ + 4 x⁴ y⁴ + 2 x⁴ y⁴ - 4 x² y⁶ - 4 x⁶ y²