`a) 6(2x-1)^2 + 5(x-2)(x+3) - 2(5-2x)^2`
`= 6(4x^2 - 4x + 1) + 5(x-2)(x+3) - 2(5-2x)^2`
`= 6(4x^2-4x+1) + 5(x-2)(x+3) - 2(25-20x+4x^2)`
`= 24x^2 - 24x + 6 + 5x^2 + 5x - 30 - 2(25-20x+4x^2)`
`= 24x^2 - 24x + 6 + 5x^2 - 30 - 50 + 40x - 8x^2`
`= 21x^2 + 21x - 74`
`b) (9x-1)^2 + (1-5x)^2 + 2(9x-1)(1-5x)`
`= 81x^2 - 18x + 1 + (1-5x)^2 + 2(9x-1)(1-5x)`
`= 81x^2 - 18x + 1 + 1 - 10x + 25x^2 +2(9x-1)(1-5x)`
`= 81x^2 - 18x + 1 + 1 - 10x + 25x^2 - 90x^2 + 28x - 2`
`= 16x^2`
`c) (x^2-5x+1)^2 + 2(5x-1)(x^2-5x+1)+(5x-1)^2`
`= (x^2-5x+1)(x^2-5x+1) + 2(5x-1)(x^2-5x+1) + 25x^2 - 10x + 1`
`= x^4 - 10x^3 + 27x^2 - 10x + 1 + 2(5x-1)(x^2-5x+1)+25x^2 - 10x + 1`
`= x^4 - 10x^3 + 27x^2 - 10x + 1 + 10x^3 - 52x^2 + 20x - 2 + 25x^2 - 10x + 1`
`= x^4`