Answer :
To find the product [tex]\((7x^2)(2x^3+5)(x^2-4x-9)\)[/tex], follow these steps:
1. Distribute:
First, we'll distribute [tex]\(7x^2\)[/tex] into the expression [tex]\((2x^3 + 5)\)[/tex]. This means we'll multiply [tex]\(7x^2\)[/tex] by each term inside the parentheses:
[tex]\[
7x^2 \times (2x^3 + 5) = (7x^2 \times 2x^3) + (7x^2 \times 5)
\][/tex]
Perform the multiplication:
[tex]\[
14x^5 + 35x^2
\][/tex]
2. Multiply the result by the third expression:
Now, multiply [tex]\((14x^5 + 35x^2)\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex].
Expand this product by distributing each term in [tex]\((14x^5 + 35x^2)\)[/tex] with every term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- Multiply [tex]\(14x^5\)[/tex] by 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]
- Next, multiply [tex]\(35x^2\)[/tex] by 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 like terms:
Form the final expression by adding all these results together:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
Thus, the product of the expression [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]
1. Distribute:
First, we'll distribute [tex]\(7x^2\)[/tex] into the expression [tex]\((2x^3 + 5)\)[/tex]. This means we'll multiply [tex]\(7x^2\)[/tex] by each term inside the parentheses:
[tex]\[
7x^2 \times (2x^3 + 5) = (7x^2 \times 2x^3) + (7x^2 \times 5)
\][/tex]
Perform the multiplication:
[tex]\[
14x^5 + 35x^2
\][/tex]
2. Multiply the result by the third expression:
Now, multiply [tex]\((14x^5 + 35x^2)\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex].
Expand this product by distributing each term in [tex]\((14x^5 + 35x^2)\)[/tex] with every term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- Multiply [tex]\(14x^5\)[/tex] by 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]
- Next, multiply [tex]\(35x^2\)[/tex] by 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 like terms:
Form the final expression by adding all these results together:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
Thus, the product of the expression [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]
