Answer :
To find the product of the expressions [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], let's break down the multiplication step-by-step:
### Step 1: Multiply the first two expressions
First, consider the multiplication of the expression [tex]\(7x^2\)[/tex] with [tex]\((2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] across each term in the parentheses:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, the result of this multiplication is:
[tex]\[14x^5 + 35x^2\][/tex]
### Step 2: Multiply the result with the third expression
Now, we need to multiply the resulting expression [tex]\( (14x^5 + 35x^2) \)[/tex] by the third expression [tex]\((x^2 - 4x - 9)\)[/tex].
Distribute each term in [tex]\( (14x^5 + 35x^2) \)[/tex] across each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
1. 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]
2. 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]
Combine all the terms from the multiplication:
[tex]\[ 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2 \][/tex]
This is the product of the three expressions.
### Step 1: Multiply the first two expressions
First, consider the multiplication of the expression [tex]\(7x^2\)[/tex] with [tex]\((2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] across each term in the parentheses:
- [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]
So, the result of this multiplication is:
[tex]\[14x^5 + 35x^2\][/tex]
### Step 2: Multiply the result with the third expression
Now, we need to multiply the resulting expression [tex]\( (14x^5 + 35x^2) \)[/tex] by the third expression [tex]\((x^2 - 4x - 9)\)[/tex].
Distribute each term in [tex]\( (14x^5 + 35x^2) \)[/tex] across each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
1. 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]
2. 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]
Combine all the terms from the multiplication:
[tex]\[ 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2 \][/tex]
This is the product of the three expressions.
