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Answer :
We start with the product
[tex]$$
(9x + 7)\left(3x^2 + 5x - 1\right).
$$[/tex]
To multiply these two expressions, we apply the distributive property (also known as the FOIL method for binomials) by multiplying each term in the first factor by each term in the second factor.
1. Multiply the term [tex]\(9x\)[/tex] by each term of the second factor:
- [tex]\(9x \times 3x^2 = 27x^3\)[/tex],
- [tex]\(9x \times 5x = 45x^2\)[/tex],
- [tex]\(9x \times (-1) = -9x\)[/tex].
2. Multiply the term [tex]\(7\)[/tex] by each term of the second factor:
- [tex]\(7 \times 3x^2 = 21x^2\)[/tex],
- [tex]\(7 \times 5x = 35x\)[/tex],
- [tex]\(7 \times (-1) = -7\)[/tex].
Now, we write all these products together:
[tex]$$
27x^3 + 45x^2 - 9x + 21x^2 + 35x - 7.
$$[/tex]
Next, we combine like terms:
- For the [tex]\(x^3\)[/tex] term, we have only: [tex]\(27x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(45x^2 + 21x^2 = 66x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms: [tex]\(-9x + 35x = 26x\)[/tex].
- The constant term is [tex]\(-7\)[/tex].
Thus, the final expanded form is:
[tex]$$
27x^3 + 66x^2 + 26x - 7.
$$[/tex]
So, the correct result of the multiplication is
[tex]$$
\boxed{27x^3 + 66x^2 + 26x - 7}.
$$[/tex]
[tex]$$
(9x + 7)\left(3x^2 + 5x - 1\right).
$$[/tex]
To multiply these two expressions, we apply the distributive property (also known as the FOIL method for binomials) by multiplying each term in the first factor by each term in the second factor.
1. Multiply the term [tex]\(9x\)[/tex] by each term of the second factor:
- [tex]\(9x \times 3x^2 = 27x^3\)[/tex],
- [tex]\(9x \times 5x = 45x^2\)[/tex],
- [tex]\(9x \times (-1) = -9x\)[/tex].
2. Multiply the term [tex]\(7\)[/tex] by each term of the second factor:
- [tex]\(7 \times 3x^2 = 21x^2\)[/tex],
- [tex]\(7 \times 5x = 35x\)[/tex],
- [tex]\(7 \times (-1) = -7\)[/tex].
Now, we write all these products together:
[tex]$$
27x^3 + 45x^2 - 9x + 21x^2 + 35x - 7.
$$[/tex]
Next, we combine like terms:
- For the [tex]\(x^3\)[/tex] term, we have only: [tex]\(27x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(45x^2 + 21x^2 = 66x^2\)[/tex].
- For the [tex]\(x\)[/tex] terms: [tex]\(-9x + 35x = 26x\)[/tex].
- The constant term is [tex]\(-7\)[/tex].
Thus, the final expanded form is:
[tex]$$
27x^3 + 66x^2 + 26x - 7.
$$[/tex]
So, the correct result of the multiplication is
[tex]$$
\boxed{27x^3 + 66x^2 + 26x - 7}.
$$[/tex]
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