Answer:
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
Explanation:
To find the product, we need to multiply the terms inside the brackets:
[7x^2][2x^3 + 5][x^2 - 4x - 9]
First, let's multiply the terms inside the second set of brackets:
[7x^2][(2x^3)(x^2) + (2x^3)(-4x) + (2x^3)(-9) + (5)(x^2) + (5)(-4x) + (5)(-9)]
Simplifying further:
[7x^2][2x^5 - 8x^4 - 18x^3 + 5x^2 - 20x - 45]
Finally, let's distribute the remaining terms:
(7x^2)(2x^5) + (7x^2)(-8x^4) + (7x^2)(-18x^3) + (7x^2)(5x^2) + (7x^2)(-20x) + (7x^2)(-45)
Simplifying each term:
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
Therefore, the product is 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.