Answer :
To find the product of the given expressions, follow these steps:
1. Identify Each Expression:
The expressions given are:
- [tex]\( 7x^2 \)[/tex]
- [tex]\( 2x^3 + 5 \)[/tex]
- [tex]\( x^2 - 4x - 9 \)[/tex]
2. Multiply the Expressions Step-by-Step:
First, we multiply the first two expressions:
[tex]\[
(7x^2)(2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
- [tex]\( 7x^2 \cdot 2x^3 = 14x^5 \)[/tex]
- [tex]\( 7x^2 \cdot 5 = 35x^2 \)[/tex]
So, the result of the first multiplication is:
[tex]\[
14x^5 + 35x^2
\][/tex]
3. Multiply the Result with the Third Expression:
Now multiply [tex]\( (14x^5 + 35x^2) \)[/tex] by [tex]\( (x^2 - 4x - 9) \)[/tex]:
[tex]\[
(14x^5 + 35x^2)(x^2 - 4x - 9)
\][/tex]
Distribute each term from the first expression through the second expression:
- [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]
4. Combine Like Terms:
Now add all these results together:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the expanded form of the product. Thus, the product of the given expressions is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This matches the result provided, confirming the solution.
1. Identify Each Expression:
The expressions given are:
- [tex]\( 7x^2 \)[/tex]
- [tex]\( 2x^3 + 5 \)[/tex]
- [tex]\( x^2 - 4x - 9 \)[/tex]
2. Multiply the Expressions Step-by-Step:
First, we multiply the first two expressions:
[tex]\[
(7x^2)(2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
- [tex]\( 7x^2 \cdot 2x^3 = 14x^5 \)[/tex]
- [tex]\( 7x^2 \cdot 5 = 35x^2 \)[/tex]
So, the result of the first multiplication is:
[tex]\[
14x^5 + 35x^2
\][/tex]
3. Multiply the Result with the Third Expression:
Now multiply [tex]\( (14x^5 + 35x^2) \)[/tex] by [tex]\( (x^2 - 4x - 9) \)[/tex]:
[tex]\[
(14x^5 + 35x^2)(x^2 - 4x - 9)
\][/tex]
Distribute each term from the first expression through the second expression:
- [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]
4. Combine Like Terms:
Now add all these results together:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the expanded form of the product. Thus, the product of the given expressions is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This matches the result provided, confirming the solution.
