(x-1)² (5x-2y²)

To expand the expression (x-1)² (5x-2y²), we can use the distributive property twice.

First, we expand (x-1)²:

(x-1)² = (x-1) * (x-1) = x(x-1) - 1(x-1) = x² - x - x + 1 = x² - 2x + 1

Next, we multiply the result above by (5x-2y²):

(x² - 2x + 1)(5x-2y²) = 5x(x²) - 2y²(x²) - 2x(5x) + 5x(-2x) + 1(5x) - 1(2y²)

simplifying further we get:

= 5x³ - 2x²y² - 10x² + 10x² - 2xy² + 5x - 2y²

= 5x³ - 2x²y² - 2xy² + 5x - 2y²