F. 2. Math Factorization

X(2XY^2-Y^2)-Y(X^2 - 2X^3)
=XY^2(2X-1)-YX^2(1-2X)
=XY^2(2X-1)+YX^2(2X-1)
=(2X-1)(XY^2+YX^2)
=XY(2X-1)(Y+X)
FINE!

X(2XY^2-Y^2)-Y(X^2 - 2X^3)

= XY(2XY - Y) - XY (X - 2X^2) <--- 先抽Y出黎

= XY[( 2XY - Y) - (X - 2X^2)] <---- 抽晒XY出去

= XY ( 2XY - Y - X + 2X^2) <--- 解開個括號, 2X^2前面變左+

= XY (2XY + 2X^2 - Y - X) <--- 執位

= XY [ (2XY + 2X^2) - (Y + X)] <---- 加番個括號, 留意後面個 X前面係 +

= XY [ 2X(Y + X ) - 1(Y+X)] <----- 前面果舊抽個2X出黎, 後面就抽1, (Y+ X) 之前果個1應該唔寫既, 但我寫埋出黎比你睇得清楚D

= XY ( 2X -1) (Y + X) <--- 答案

希望幫到你~