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Answer :
To find the product [tex]\(\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)\)[/tex], we will multiply these expressions together step by step to reach the simplified result.
1. Multiply the first two expressions:
- Start with [tex]\((7x^2)(2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] across each term inside the parentheses:
- [tex]\(7x^2 \times 2x^3 = 14x^{5}\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- Combine these to get:
[tex]\[
14x^5 + 35x^2
\][/tex]
2. Multiply the result by the third expression:
- Now, take [tex]\((14x^5 + 35x^2)\)[/tex] and multiply it by [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute each term in [tex]\(14x^5 + 35x^2\)[/tex] across every term in [tex]\(x^2 - 4x - 9\)[/tex]:
- [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]
- Combine all these terms:
[tex]\[
14x^{7} - 56x^{6} - 126x^{5} + 35x^{4} - 140x^{3} - 315x^{2}
\][/tex]
By following these steps, we obtain the final simplified product:
[tex]\[
14x^{7} - 56x^{6} - 126x^{5} + 35x^{4} - 140x^{3} - 315x^{2}
\][/tex]
This is the result of multiplying the given expressions together.
1. Multiply the first two expressions:
- Start with [tex]\((7x^2)(2x^3 + 5)\)[/tex].
- Distribute [tex]\(7x^2\)[/tex] across each term inside the parentheses:
- [tex]\(7x^2 \times 2x^3 = 14x^{5}\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- Combine these to get:
[tex]\[
14x^5 + 35x^2
\][/tex]
2. Multiply the result by the third expression:
- Now, take [tex]\((14x^5 + 35x^2)\)[/tex] and multiply it by [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute each term in [tex]\(14x^5 + 35x^2\)[/tex] across every term in [tex]\(x^2 - 4x - 9\)[/tex]:
- [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]
- Combine all these terms:
[tex]\[
14x^{7} - 56x^{6} - 126x^{5} + 35x^{4} - 140x^{3} - 315x^{2}
\][/tex]
By following these steps, we obtain the final simplified product:
[tex]\[
14x^{7} - 56x^{6} - 126x^{5} + 35x^{4} - 140x^{3} - 315x^{2}
\][/tex]
This is the result of multiplying the given expressions together.
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