a/ (9x-1)² + (1 - 5x) ² + 2(9x - 1)(1 - 5x)
= (9x - 1)² + 2(9x - 1)(1 - 5x) + (1 - 5x)²
= (9x - 1 + 1 - 5x)²
= (4x)²
= 16x²
b/ (a + b + c) ² + ( a + b - c) ² - 2(a + b)²
= [(a+b)+c]² + [(a+b)-c]² - 2(a +b)²
= (a +b)² + 2(a+b)c + c² + (a+b)² - 2(a+b)c + c² - 2(a+b)²
= 2(a+b)² - 2(a+b)² + 2c²
= 2c²
c/ (2a ² + 2a + 1) ( 2a ² - 2a + 1) - (2a ² + 1) ²
= (2a² + 1 + 2a)(2a² + 1 - 2a) - (2a² + 1)²
= (2a² + 1)² - (2a)² - (2a² + 1)²
= (2a² + 1)² - (2a² + 1)² - 4a²
= -4a²
d/ 6(x+1) ² - 2(x+1) ² + 2(x-1)(x ² + x +1) -1
= 4(x + 1)² + 2(x³ - 1) - 1
= 4(x² + 2x + 1) + 2(x³ - 1) - 1
= 4x² + 8x + 4 + 2x³ - 2 - 1
= 2x³ + 4x² + 8x + 1