Use the binomial pattern to write the expansion for (x+y)6

Question

I really don't know what this question means. Please help!

Answer 1

(x + y)⁶ = ₆C₀x⁶y⁰ + ₆C₁x⁵y¹ + ₆C₂x⁴y² + ₆C₃x³y³ + ₆C₄x²y⁴ + ₆C₅x¹y⁵ + ₆C₆x⁰y⁶

= x⁶ + 6x⁵y + 15x⁴y² + 20x³y³ + 15x²y⁴ + 6xy⁵ + y⁶

In the expansion of (x + y)ⁿ each term has the form _nC_rx^n-ry^r, where:

_nC_r = n choose r = n! / [r! (n-r)!]