Question:

Expand (1-3x)^10 up to and including the term x². Deduce the coefficient of x² in the expansion of (1+3x)^2(1-3x)^10.

Attempt:

(1-3x)^10 = 10C0*1^10 + 10C1*1^9*(-3x) + 10C2*1^8*(-3x)^2 +.....

(1-3x)^10 = 1*1 + 10*1*(-3x) + 45*1*(-3x)^2 +.....

(1-3x)^10 = 1 - 30x + 405x² +.....

(1+3x)^2 = 2C0*1^2 + 2C1*1*(3x) + 2C2*(3x)²

(1+3x)^2 = 1*1 + 2*1*3x + 1*9x²

(1+3x)^2 = 1 + 6x + 9x²

= (1 + 6x + 9x²)(1 - 30x + 405x² +.....)

Coefficient of x² = 405 + 180 + 9

Coefficient of x² = 594

Answer in textbook is234, what is wrong?