Answer :
To find the product [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we'll break it down into smaller steps.
1. Multiply the first two expressions: [tex]\((7x^2)\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] across each term in the second expression:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, the result is: [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result from step 1 by the third expression: [tex]\( (14x^5 + 35x^2)(x^2 - 4x - 9) \)[/tex].
- Distribute each term in [tex]\((14x^5 + 35x^2)\)[/tex] to each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [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]
3. Combine like terms:
After distributing, our expression is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
There are no like terms to combine, so this is our final product.
Thus, the product of [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. Multiply the first two expressions: [tex]\((7x^2)\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] across each term in the second expression:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, the result is: [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result from step 1 by the third expression: [tex]\( (14x^5 + 35x^2)(x^2 - 4x - 9) \)[/tex].
- Distribute each term in [tex]\((14x^5 + 35x^2)\)[/tex] to each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [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]
3. Combine like terms:
After distributing, our expression is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
There are no like terms to combine, so this is our final product.
Thus, the product of [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]
