Here are the answers for the blank spots in each question:
**Question 1**
(4x³ + 2x²)(6x − 9) = **24x⁴ - 36x³ + 12x² - 18x²**
Simplifying further: = **24x⁴ - 36x³ - 6x²**
**Question 2**
(5y² − 6y)(7y⁷ − y³) = **35y⁹ - 5y⁵ - 42y⁸ + 6y⁴**
Final answer (combining terms where possible): = **35y⁹ - 42y⁸ - 5y⁵ + 6y⁴**
**Question 3**
3x²(2x⁴ − 15x) = **6x⁶ - 45x³**
**Question 4**
(3x² − 8)(4x² + 7) = **12x⁴ + 21x² - 32**
**Question 5**
(−3x⁵ − 4x⁴)(7x² − 2x + 6) = **-21x⁷ + 6x⁵ + 8x⁶ - 12x⁴ - 24x⁴**
Final answer (combining terms where possible): = **-21x⁷ + 8x⁶ - 18x⁴ + 6x⁵**
Feel free to ask if you need any further clarification!