Answer :
To find the product of the given expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we'll follow these steps:
1. Multiply the first two terms: [tex]\((7x^2)\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Start by distributing [tex]\(7x^2\)[/tex] into each term of [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \times 2x^3 = 14x^5
\][/tex]
[tex]\[
7x^2 \times 5 = 35x^2
\][/tex]
So, the product of [tex]\((7x^2)(2x^3 + 5)\)[/tex] is:
[tex]\[
14x^5 + 35x^2
\][/tex]
2. Multiply the result from step 1 by the third term: [tex]\((x^2 - 4x - 9)\)[/tex].
Now, distribute each term from [tex]\(14x^5 + 35x^2\)[/tex] into [tex]\(x^2 - 4x - 9\)[/tex]:
- Multiply [tex]\(14x^5\)[/tex] with each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
14x^5 \times x^2 = 14x^7
\][/tex]
[tex]\[
14x^5 \times (-4x) = -56x^6
\][/tex]
[tex]\[
14x^5 \times (-9) = -126x^5
\][/tex]
- Multiply [tex]\(35x^2\)[/tex] with each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
35x^2 \times x^2 = 35x^4
\][/tex]
[tex]\[
35x^2 \times (-4x) = -140x^3
\][/tex]
[tex]\[
35x^2 \times (-9) = -315x^2
\][/tex]
3. Combine all the terms:
Combine the results from the multiplication:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This results in the final product:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
And that's the product of the given expression.
1. Multiply the first two terms: [tex]\((7x^2)\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Start by distributing [tex]\(7x^2\)[/tex] into each term of [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \times 2x^3 = 14x^5
\][/tex]
[tex]\[
7x^2 \times 5 = 35x^2
\][/tex]
So, the product of [tex]\((7x^2)(2x^3 + 5)\)[/tex] is:
[tex]\[
14x^5 + 35x^2
\][/tex]
2. Multiply the result from step 1 by the third term: [tex]\((x^2 - 4x - 9)\)[/tex].
Now, distribute each term from [tex]\(14x^5 + 35x^2\)[/tex] into [tex]\(x^2 - 4x - 9\)[/tex]:
- Multiply [tex]\(14x^5\)[/tex] with each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
14x^5 \times x^2 = 14x^7
\][/tex]
[tex]\[
14x^5 \times (-4x) = -56x^6
\][/tex]
[tex]\[
14x^5 \times (-9) = -126x^5
\][/tex]
- Multiply [tex]\(35x^2\)[/tex] with each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
35x^2 \times x^2 = 35x^4
\][/tex]
[tex]\[
35x^2 \times (-4x) = -140x^3
\][/tex]
[tex]\[
35x^2 \times (-9) = -315x^2
\][/tex]
3. Combine all the terms:
Combine the results from the multiplication:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This results in the final product:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
And that's the product of the given expression.
