Use the Binomial Theorem to expand and simplify the expression.

Question

Use the Binomial Theorem to expand and simplify the expression (x² + y²)³

Answer 1

(x² + y²)³ = (1)(x²)³(y²)⁰ + 3(x²)²(y²) + 3(x²)(y²)² + (1)(x²)⁰(y²)³

= x⁶ + 3x⁴y² + 3x²y⁴ + y⁶

Answer 2

(x² + y²)³ = (x²)³(y²)⁰ + 3[(x²)²(y²)¹] + 3[(x²)¹(y²)²] + (x²)⁰(y²)³

= x⁶y⁰ + 3(x⁴y²)+ 3(x²y⁴)+ x⁰y⁶

= x⁶(1) + 3x⁴y²+ 3x²y⁴+ (1)y⁶

= x⁶ + 3x⁴y²+ 3x²y⁴+ y⁶