<span lang="EN-US

In expression a⁴ – (b + c)⁴

Both terms are perfect square

⇒ a⁴ = a² × a²

⇒ (b + c)⁴ = (b + c)² × (b + c)²

∴ a⁴ – (b + c)⁴ Seems to be in identity a²-b² = (a + b)(a-b)

Where a = a² and b = (b + c)²;

a⁴ – (b + c)⁴ = (a² – (b + c)²)( a² + (b + c)²),

∴ a² – (b + c)² Seems to be in identity a²-b² = (a + b)(a-b)

Where a = a and b = (b + c);

a² – (b + c)² = (a– (b + c))( a+ (b + c)),

⇒ a⁴ – (b + c)⁴ = (a– (b + c))( a+ (b + c)), ( a² + (b + c)²)

⇒ a⁴ – (b + c)⁴ = (a–b–c)(a + b + c), (a² + b² + c² + 2bc)

Hence the factors of a⁴ – (b + c)⁴ are (a–b–c),(a + b + c),( a² + b² + c² + 2bc)