answer is 8x+24
area of vanessa's patio = length × width
given, length = (3x² + 5x + 10)
width = (x² - 3x - 1)
area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)
= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)
= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10
= 3x⁴ - 4x³ - 8x² - 35x - 10
hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)