How do you solve (x^2y+3)^7

Question

The equation has multiplying and adding exponents with variables

Answer 1

(x²y+3)⁷.

First we need the coefficients from Pascal's Triangle: 1, 7, 21, 35, 35, 21, 7, 1.

Next we expand (a+b)⁷, using these coefficients:

a⁷+7a⁶b+21a⁵b²+35a⁴b³+35a³b⁴+21a²b⁵+7ab⁶+b⁷.

Let a=x²y and b=3:

x¹⁴y⁷+7x¹²y⁶(3)+21x¹⁰y⁵(3²)+35x⁸y⁴(3³)+35x⁶y³(3⁴)+21x⁴y²(3⁵)+7x²y(3⁶)+3⁷,

x¹⁴y⁷+21x¹²y⁶+189x¹⁰y⁵+35x⁸y⁴(3³)+945x⁶y³+5103x⁴y²+5103x²y+2187.