Answer :
To find the product of the expressions [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we'll multiply these expressions step-by-step.
### Step 1: Multiply the first two expressions
First, we multiply [tex]\(7x^2\)[/tex] by [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \cdot (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
Calculate each term:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, the result of the multiplication of the first two expressions is:
[tex]\[
14x^5 + 35x^2
\][/tex]
### Step 2: Multiply the result by the third expression
Now, multiply the result [tex]\(14x^5 + 35x^2\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \cdot (x^2 - 4x - 9)
\][/tex]
Distribute each term of the first expression to each term of the second expression:
- [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]
- [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]
Combine all these terms:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
Therefore, the product of the expressions [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex] is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
### Step 1: Multiply the first two expressions
First, we multiply [tex]\(7x^2\)[/tex] by [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \cdot (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
Calculate each term:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, the result of the multiplication of the first two expressions is:
[tex]\[
14x^5 + 35x^2
\][/tex]
### Step 2: Multiply the result by the third expression
Now, multiply the result [tex]\(14x^5 + 35x^2\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \cdot (x^2 - 4x - 9)
\][/tex]
Distribute each term of the first expression to each term of the second expression:
- [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]
- [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]
Combine all these terms:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
Therefore, the product of the expressions [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex] is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
