Question

(x-2)^3+(x-3)^3+(5-2x)^3 PDTTNT

Answer 1

(x - 2)³ + (x - 3)³ + (5 - 2x)³

= x³ - 6x² + 12x - 8 + x³ - 9x² + 27x - 27 + 125 - 150x + 60x² - 8x³

= -6x³ + 45x² - 111x + 90

= -6x³ + 12x² + 33x² - 66x - 45x + 90

= (-6x³ + 12x²) + (33x² - 66x) - (45x - 90)

= -6x²(x - 2) + 33x(x - 2) - 45(x - 2)

= (x - 2)(-6x² + 33x - 45)

= (x - 2)(-6x² + 18x + 15x - 45)

= (x - 2)[(-6x² + 18x) + (15x - 45)]

= (x - 2)[-6x(x - 3) + 15(x - 3)]

= (x - 2)(x - 3)(-6x + 15)

= -3(x - 2)(x - 3)(2x - 5)