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Answer :
To find the product of the expression [tex]\(\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)\)[/tex], we'll break it down into clear steps:
1. Distribute the first two expressions:
Start by multiplying [tex]\(7x^2\)[/tex] and [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \times (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
So, the result is [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
Now take [tex]\((14x^5 + 35x^2)\)[/tex] and multiply it by [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \times (x^2 - 4x - 9)
\][/tex]
Distribute each term of [tex]\(14x^5 + 35x^2\)[/tex] separately over [tex]\(x^2 - 4x - 9\)[/tex]:
- Multiply [tex]\(14x^5\)[/tex] by each 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]
- Multiply [tex]\(35x^2\)[/tex] by each term in [tex]\((x^2 - 4x - 9)\)[/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 terms:
Combine all these products to get the final polynomial:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This polynomial is the product of the given expressions.
1. Distribute the first two expressions:
Start by multiplying [tex]\(7x^2\)[/tex] and [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \times (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
- [tex]\(7x^2 \times 2x^3 = 14x^5\)[/tex]
- [tex]\(7x^2 \times 5 = 35x^2\)[/tex]
So, the result is [tex]\(14x^5 + 35x^2\)[/tex].
2. Multiply the result with the third expression:
Now take [tex]\((14x^5 + 35x^2)\)[/tex] and multiply it by [tex]\((x^2 - 4x - 9)\)[/tex]:
[tex]\[
(14x^5 + 35x^2) \times (x^2 - 4x - 9)
\][/tex]
Distribute each term of [tex]\(14x^5 + 35x^2\)[/tex] separately over [tex]\(x^2 - 4x - 9\)[/tex]:
- Multiply [tex]\(14x^5\)[/tex] by each 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]
- Multiply [tex]\(35x^2\)[/tex] by each term in [tex]\((x^2 - 4x - 9)\)[/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 terms:
Combine all these products to get the final polynomial:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]
This polynomial is the product of the given expressions.
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