(2x-y)(y+2x)+x(4-3x)....5c(c+1)-(b-3c)(b+3x).......(y-2)(y+2)+(3-y)(3+y)

1

(2x - y)(y + 2x) + x(4 - 3x) = 2х * у + 2х * 2х - у * у - у * 2х + х * 4 - х * 3х = 2ху + 4x^2 - y^2 - 2xy + 4x - 3x^2 = 4x^2 - 3x^2 - y^2 + 2ху - 2xy + 4x  = x^2 - y^2 + 4x. 

2

5c(c + 1) - (b - 3c)(b + 3x) = 5c * c + 5c * 1 - (b * b + b * 3x - 3c * b - 3c * 3x) = 5c * c + 5c * 1 - b * b - b * 3x + 3c * b + 3c * 3x = 5c^2 + 5c - b^2 - 3bx + 3cb + 9cx.

3

(y - 2)(y + 2) + (3 - y)(3 + y) = y * y + y * 2 - 2 * y - 2 * 2 + 3 * 3 + 3 * y - y * 3 - y * y = y^2 + 2y - 2y - 4 + 9 + 3y - 3y - y^2 = y^2  - y^2 + 2y - 2y + 3y - 3y - 4 + 9 = 5.