What is the constant term in the expansion of the binomial (x-2) ^4?

Well, since the expanded form of (x-2) ^4 is x^4-8x³+24x²-32x+16

The constant is the 4th term, since it is the integer so your answer is 16.

(x - 2) ⁴

(x - 2) ² (x - 2) ²

(x - 2) (x - 2) (x - 2) (x - 2)

(x (x) - x (2) - 2 (x) + 2 (2)) (x (x) - x (2) - 2 (x) + 2 (2))

(x² - 2x - 2x + 4) (x² - 2x - 2x + 4)

(x² - 4x + 4) (x² - 4x + 4)

x² (x² - 4x + 4) - 4x (x² - 4x + 4) + 4 (x² - 4x + 4)

x² (x²) - x² (4x) + x² (4) - 4x (x²) + 4x (4x) - 4x (4) + 4 (x²) - 4 (4x) + 4 (4)

x⁴ - 4x³ + 4x² - 4x³ + 16x² - 16x + 4x² - 16x + 16

x⁴ - 4x³ - 4x³ + 4x² + 16x² + 4x² - 16x - 16x + 16

x⁴ + 8x³ + 24x² - 32x + 16

The constant term in the expansion of the binomial is 16.