Answer :
To find the product of the given expressions [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we can follow these steps:
1. Multiply the expressions step-by-step:
Start by multiplying the first two expressions:
[tex]\((7x^2) \cdot (2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] to each term in the second expression:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, [tex]\((7x^2)(2x^3 + 5)\)[/tex] simplifies to [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].
- Distribute each term of [tex]\(14x^5 + 35x^2\)[/tex] across the terms in [tex]\(x^2 - 4x - 9\)[/tex].
For [tex]\(14x^5\)[/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]
For [tex]\(35x^2\)[/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:
Combine and organize all the terms from the distribution:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This results in the polynomial:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the expanded form of the product of the given expressions.
1. Multiply the expressions step-by-step:
Start by multiplying the first two expressions:
[tex]\((7x^2) \cdot (2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] to each term in the second expression:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, [tex]\((7x^2)(2x^3 + 5)\)[/tex] simplifies to [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].
- Distribute each term of [tex]\(14x^5 + 35x^2\)[/tex] across the terms in [tex]\(x^2 - 4x - 9\)[/tex].
For [tex]\(14x^5\)[/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]
For [tex]\(35x^2\)[/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:
Combine and organize all the terms from the distribution:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This results in the polynomial:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the expanded form of the product of the given expressions.
