Answer :
We begin with the expression
[tex]$$
(7x^2)(2x^3 + 5)(x^2 - 4x - 9).
$$[/tex]
Step 1. Multiply the first two factors
Multiply [tex]$7x^2$[/tex] by each term in [tex]$(2x^3+5)$[/tex]:
[tex]$$
7x^2 \cdot 2x^3 = 14x^5,
$$[/tex]
[tex]$$
7x^2 \cdot 5 = 35x^2.
$$[/tex]
Thus, the product of the first two factors is
[tex]$$
14x^5 + 35x^2.
$$[/tex]
Step 2. Multiply the result by the third factor
We now multiply
[tex]$$
(14x^5 + 35x^2)(x^2 - 4x - 9).
$$[/tex]
Distribute each term in [tex]$14x^5 + 35x^2$[/tex] across every term in [tex]$x^2 - 4x - 9$[/tex].
Multiplying [tex]$14x^5$[/tex] by each term:
[tex]$$
14x^5 \cdot x^2 = 14x^7,
$$[/tex]
[tex]$$
14x^5 \cdot (-4x) = -56x^6,
$$[/tex]
[tex]$$
14x^5 \cdot (-9) = -126x^5.
$$[/tex]
Multiplying [tex]$35x^2$[/tex] by each term:
[tex]$$
35x^2 \cdot x^2 = 35x^4,
$$[/tex]
[tex]$$
35x^2 \cdot (-4x) = -140x^3,
$$[/tex]
[tex]$$
35x^2 \cdot (-9) = -315x^2.
$$[/tex]
Step 3. Combine all terms
Gathering all the results, we have
[tex]$$
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
$$[/tex]
This is the final product.
Thus, the product is
[tex]$$
\boxed{14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2}.
$$[/tex]
[tex]$$
(7x^2)(2x^3 + 5)(x^2 - 4x - 9).
$$[/tex]
Step 1. Multiply the first two factors
Multiply [tex]$7x^2$[/tex] by each term in [tex]$(2x^3+5)$[/tex]:
[tex]$$
7x^2 \cdot 2x^3 = 14x^5,
$$[/tex]
[tex]$$
7x^2 \cdot 5 = 35x^2.
$$[/tex]
Thus, the product of the first two factors is
[tex]$$
14x^5 + 35x^2.
$$[/tex]
Step 2. Multiply the result by the third factor
We now multiply
[tex]$$
(14x^5 + 35x^2)(x^2 - 4x - 9).
$$[/tex]
Distribute each term in [tex]$14x^5 + 35x^2$[/tex] across every term in [tex]$x^2 - 4x - 9$[/tex].
Multiplying [tex]$14x^5$[/tex] by each term:
[tex]$$
14x^5 \cdot x^2 = 14x^7,
$$[/tex]
[tex]$$
14x^5 \cdot (-4x) = -56x^6,
$$[/tex]
[tex]$$
14x^5 \cdot (-9) = -126x^5.
$$[/tex]
Multiplying [tex]$35x^2$[/tex] by each term:
[tex]$$
35x^2 \cdot x^2 = 35x^4,
$$[/tex]
[tex]$$
35x^2 \cdot (-4x) = -140x^3,
$$[/tex]
[tex]$$
35x^2 \cdot (-9) = -315x^2.
$$[/tex]
Step 3. Combine all terms
Gathering all the results, we have
[tex]$$
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
$$[/tex]
This is the final product.
Thus, the product is
[tex]$$
\boxed{14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2}.
$$[/tex]
