Answer :
To find the product of the expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we need to multiply the three parts together step by step.
### Step 1: Multiply [tex]\(7x^2\)[/tex] with each term in the second expression [tex]\((2x^3 + 5)\)[/tex].
- Multiply: [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- Multiply: [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
So the result of this step is:
[tex]\[14x^5 + 35x^2\][/tex]
### Step 2: Multiply the result from Step 1, [tex]\((14x^5 + 35x^2)\)[/tex], with the third expression [tex]\((x^2 - 4x - 9)\)[/tex].
- Multiply: [tex]\(14x^5 \times x^2 = 14x^7\)[/tex]
- Multiply: [tex]\(14x^5 \times (-4x) = -56x^6\)[/tex]
- Multiply: [tex]\(14x^5 \times (-9) = -126x^5\)[/tex]
Now, do the same with the second term from Step 1, [tex]\(35x^2\)[/tex]:
- Multiply: [tex]\(35x^2 \times x^2 = 35x^4\)[/tex]
- Multiply: [tex]\(35x^2 \times (-4x) = -140x^3\)[/tex]
- Multiply: [tex]\(35x^2 \times (-9) = -315x^2\)[/tex]
Combine all these products together:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]
This is the expanded form of the original expression, and thus it is the product we are looking for.
### Step 1: Multiply [tex]\(7x^2\)[/tex] with each term in the second expression [tex]\((2x^3 + 5)\)[/tex].
- Multiply: [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- Multiply: [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
So the result of this step is:
[tex]\[14x^5 + 35x^2\][/tex]
### Step 2: Multiply the result from Step 1, [tex]\((14x^5 + 35x^2)\)[/tex], with the third expression [tex]\((x^2 - 4x - 9)\)[/tex].
- Multiply: [tex]\(14x^5 \times x^2 = 14x^7\)[/tex]
- Multiply: [tex]\(14x^5 \times (-4x) = -56x^6\)[/tex]
- Multiply: [tex]\(14x^5 \times (-9) = -126x^5\)[/tex]
Now, do the same with the second term from Step 1, [tex]\(35x^2\)[/tex]:
- Multiply: [tex]\(35x^2 \times x^2 = 35x^4\)[/tex]
- Multiply: [tex]\(35x^2 \times (-4x) = -140x^3\)[/tex]
- Multiply: [tex]\(35x^2 \times (-9) = -315x^2\)[/tex]
Combine all these products together:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]
This is the expanded form of the original expression, and thus it is the product we are looking for.
