Answer :
To find the product [tex]\(\left(7 x^2\right)\left(2 x^3+5\right)\left(x^2-4 x-9\right)\)[/tex], we need to multiply these expressions together. Let's break it down step-by-step.
1. Multiply the first two expressions:
Start by multiplying [tex]\(7x^2\)[/tex] and [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \times (2x^3 + 5) = 7x^2 \times 2x^3 + 7x^2 \times 5
\][/tex]
Simplify each term:
[tex]\[
= 14x^5 + 35x^2
\][/tex]
Now, the product of the first two expressions is [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
Now take the result [tex]\(14x^5 + 35x^2\)[/tex] and multiply it by [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \times (x^2 - 4x - 9)
\][/tex]
Distribute each term in [tex]\((14x^5 + 35x^2)\)[/tex] through [tex]\((x^2 - 4x - 9)\)[/tex]:
1. [tex]\(14x^5 \times (x^2 - 4x - 9)\)[/tex]:
[tex]\[
= 14x^5 \times x^2 - 14x^5 \times 4x - 14x^5 \times 9
\][/tex]
[tex]\[
= 14x^7 - 56x^6 - 126x^5
\][/tex]
2. [tex]\(35x^2 \times (x^2 - 4x - 9)\)[/tex]:
[tex]\[
= 35x^2 \times x^2 - 35x^2 \times 4x - 35x^2 \times 9
\][/tex]
[tex]\[
= 35x^4 - 140x^3 - 315x^2
\][/tex]
3. Combine all the terms:
Bring together all the terms from the multiplication calculations:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the product of the given expressions.
1. Multiply the first two expressions:
Start by multiplying [tex]\(7x^2\)[/tex] and [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \times (2x^3 + 5) = 7x^2 \times 2x^3 + 7x^2 \times 5
\][/tex]
Simplify each term:
[tex]\[
= 14x^5 + 35x^2
\][/tex]
Now, the product of the first two expressions is [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
Now take the result [tex]\(14x^5 + 35x^2\)[/tex] and multiply it by [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \times (x^2 - 4x - 9)
\][/tex]
Distribute each term in [tex]\((14x^5 + 35x^2)\)[/tex] through [tex]\((x^2 - 4x - 9)\)[/tex]:
1. [tex]\(14x^5 \times (x^2 - 4x - 9)\)[/tex]:
[tex]\[
= 14x^5 \times x^2 - 14x^5 \times 4x - 14x^5 \times 9
\][/tex]
[tex]\[
= 14x^7 - 56x^6 - 126x^5
\][/tex]
2. [tex]\(35x^2 \times (x^2 - 4x - 9)\)[/tex]:
[tex]\[
= 35x^2 \times x^2 - 35x^2 \times 4x - 35x^2 \times 9
\][/tex]
[tex]\[
= 35x^4 - 140x^3 - 315x^2
\][/tex]
3. Combine all the terms:
Bring together all the terms from the multiplication calculations:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the product of the given expressions.
