a) 2x² + 3(x-1)(x + 1) - 5x(x+1)
= 2x² + 3(x² - 1) - 5x² - 5x
= 2x² + 3x² - 3 - 5x² - 5x
= (2x² + 3x² - 5x²) + (-5x - 3)
= 0x² - 5x - 3 = -5x - 3
b) (8-5x)(x+2) + 4(x-2)(x+1) + 2(x-2)(x+2) + 10
= 8x + 16 - 5x² - 10x + 4x² - 8 + 2x² - 4 + 2x² + 4x + 10
= (8x - 10x + 4x + 4x) + (16 - 8 - 4 + 10) + (-5x² + 4x² + 2x²)
= 6x + 14 + x²
= x² + 6x + 14
c) 4(x - 1)(x+5) - (x + 2)(x+5) - 3(x-1)(x + 2)
= 4x² + 20x - 4 - (x² + 7x + 10) - 3x² + 3 - 3x² + 3x
= 4x² + 20x - 4 - x² - 7x - 10 - 3x² + 3 - 3x² + 3x
= (4x² - x² - 3x² - 3x²) + (20x - 7x + 3x) + (-4 - 10 + 3)
= -3x² + 16x - 11
d) (x² + x^y + y²¹)(x - y)(x³ + y³¹) = (x³ - xy + x^y²¹ - yx² - y^²¹x + y³¹)(x³ + y³¹)
= x³ * x³ + x³ * y³¹ - xy * x³ - xy * y³¹ + x^y²¹ * x³ + x^y²¹ * y³¹ - yx² * x³ - yx² * y³¹ - y^²¹x * x³ - y^²¹x * y³¹ + y³¹ * x³ + y³¹ * y³¹
= x^6 + x³y³¹ - x^4y - xy^³¹ + x^y²¹x³ + x^y²¹y³¹ - yx²x³ - yx²y³¹ - y^²¹x^³ - y^²¹xy³¹ + y³¹x³ + y⁴¹
= x^6 + x³y³¹ - x^4y - xy^³¹ + x^(y+3) + x^(y+3)y³¹ - yx²x³ - yx²y³¹ - y^²¹x^³ - y^²¹xy³¹ + y³¹x³ + y⁴¹