Explanation:
we get
(x + 2y)⁷ out of
(x + y)⁷ by setting y = 2y
(x + y)⁷ is defined by the binomial expansion theorem :
x⁷ + 7x⁶y + 21x⁵y² + 35x⁴y³ + 35x³y⁴ + 21x²y⁵ + 7xy⁶ + y⁷
now we replace every y by 2y :
x⁷+7x⁶2y+21x⁵(2y)²+35x⁴(2y)³+35x³(2y)⁴+21x²(2y)⁵+7x(2y)⁶ + (2y)⁷
x⁷ + 14x⁶y + 84x⁵y² + 280x⁴y³ + 560x³y⁴ + 672x²y⁵ + 448xy⁶ + 128y⁷