Answer :
To find the product of the expressions [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we can follow these steps:
1. Multiply the first two expressions:
- Start with [tex]\((7x^2)\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Use the distributive property:
[tex]\(7x^2 \cdot (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5\)[/tex].
- Simplify each term:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex].
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex].
So, the result of multiplying the first two expressions is:
[tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
- Now multiply [tex]\((14x^5 + 35x^2)\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex].
- Use the distributive property again for each term in the first expression:
- Multiply [tex]\(14x^5\)[/tex] by 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].
- Multiply [tex]\(35x^2\)[/tex] by each term in [tex]\((x^2 - 4x - 9)\)[/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 all the terms:
Now, list all the resulting terms together:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
\][/tex]
This is the final product of the given expressions.
1. Multiply the first two expressions:
- Start with [tex]\((7x^2)\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Use the distributive property:
[tex]\(7x^2 \cdot (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5\)[/tex].
- Simplify each term:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex].
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex].
So, the result of multiplying the first two expressions is:
[tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
- Now multiply [tex]\((14x^5 + 35x^2)\)[/tex] by [tex]\((x^2 - 4x - 9)\)[/tex].
- Use the distributive property again for each term in the first expression:
- Multiply [tex]\(14x^5\)[/tex] by 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].
- Multiply [tex]\(35x^2\)[/tex] by each term in [tex]\((x^2 - 4x - 9)\)[/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 all the terms:
Now, list all the resulting terms together:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
\][/tex]
This is the final product of the given expressions.
