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Answer :
To find the product of the given expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we'll multiply the expressions step-by-step:
1. Multiply the first two expressions:
- Start with [tex]\(7x^2\)[/tex] and distribute it across [tex]\(2x^3 + 5\)[/tex]:
[tex]\[
7x^2 \times (2x^3 + 5) = (7x^2 \times 2x^3) + (7x^2 \times 5)
\][/tex]
- Calculate each term:
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- Combine to get: [tex]\(14x^5 + 35x^2\)[/tex]
2. Multiply the result with the third expression [tex]\(x^2 - 4x - 9\)[/tex]:
- Distribute [tex]\((14x^5 + 35x^2)\)[/tex] across [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \times (x^2 - 4x - 9)
\][/tex]
- Multiply each term in the first polynomial by each term in the second polynomial:
- [tex]\(14x^5 \times x^2 = 14x^7\)[/tex]
- [tex]\(14x^5 \times -4x = -56x^6\)[/tex]
- [tex]\(14x^5 \times -9 = -126x^5\)[/tex]
- [tex]\(35x^2 \times x^2 = 35x^4\)[/tex]
- [tex]\(35x^2 \times -4x = -140x^3\)[/tex]
- [tex]\(35x^2 \times -9 = -315x^2\)[/tex]
3. Combine all the terms:
- Put together all the terms from the multiplication:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
The expanded form of the product is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the final answer for the expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex].
1. Multiply the first two expressions:
- Start with [tex]\(7x^2\)[/tex] and distribute it across [tex]\(2x^3 + 5\)[/tex]:
[tex]\[
7x^2 \times (2x^3 + 5) = (7x^2 \times 2x^3) + (7x^2 \times 5)
\][/tex]
- Calculate each term:
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- Combine to get: [tex]\(14x^5 + 35x^2\)[/tex]
2. Multiply the result with the third expression [tex]\(x^2 - 4x - 9\)[/tex]:
- Distribute [tex]\((14x^5 + 35x^2)\)[/tex] across [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \times (x^2 - 4x - 9)
\][/tex]
- Multiply each term in the first polynomial by each term in the second polynomial:
- [tex]\(14x^5 \times x^2 = 14x^7\)[/tex]
- [tex]\(14x^5 \times -4x = -56x^6\)[/tex]
- [tex]\(14x^5 \times -9 = -126x^5\)[/tex]
- [tex]\(35x^2 \times x^2 = 35x^4\)[/tex]
- [tex]\(35x^2 \times -4x = -140x^3\)[/tex]
- [tex]\(35x^2 \times -9 = -315x^2\)[/tex]
3. Combine all the terms:
- Put together all the terms from the multiplication:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
The expanded form of the product is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This is the final answer for the expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex].
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