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Answer :
To find the product of the expression [tex]\((7x^2)(2x^3+5)(x^2-4x-9)\)[/tex], we will multiply these expressions step by step.
1. Multiply the first two expressions:
- The expressions are [tex]\(7x^2\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Multiply each term in the second expression by [tex]\(7x^2\)[/tex]:
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- So, the product of these two expressions is:
[tex]\[14x^5 + 35x^2\][/tex]
2. Multiply the resulting expression by the third expression:
- The expressions are [tex]\((14x^5 + 35x^2)\)[/tex] and [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute each term in the first expression across each term in the second expression.
- For [tex]\(14x^5\)[/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]
- For [tex]\(35x^2\)[/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:
- Gather all the terms from both parts:
- [tex]\(14x^7\)[/tex]
- [tex]\(-56x^6\)[/tex]
- [tex]\(-126x^5\)[/tex]
- [tex]\(35x^4\)[/tex]
- [tex]\(-140x^3\)[/tex]
- [tex]\(-315x^2\)[/tex]
4. Write down the final expression:
- Combine and arrange the terms in descending order of exponents:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]
So, the product of [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex] is:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]
1. Multiply the first two expressions:
- The expressions are [tex]\(7x^2\)[/tex] and [tex]\((2x^3 + 5)\)[/tex].
- Multiply each term in the second expression by [tex]\(7x^2\)[/tex]:
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
- So, the product of these two expressions is:
[tex]\[14x^5 + 35x^2\][/tex]
2. Multiply the resulting expression by the third expression:
- The expressions are [tex]\((14x^5 + 35x^2)\)[/tex] and [tex]\((x^2 - 4x - 9)\)[/tex].
- Distribute each term in the first expression across each term in the second expression.
- For [tex]\(14x^5\)[/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]
- For [tex]\(35x^2\)[/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:
- Gather all the terms from both parts:
- [tex]\(14x^7\)[/tex]
- [tex]\(-56x^6\)[/tex]
- [tex]\(-126x^5\)[/tex]
- [tex]\(35x^4\)[/tex]
- [tex]\(-140x^3\)[/tex]
- [tex]\(-315x^2\)[/tex]
4. Write down the final expression:
- Combine and arrange the terms in descending order of exponents:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]
So, the product of [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex] is:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]
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