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Answer :
To multiply the expressions
$$
(9x+7)(3x^2+5x-1),
$$
we can use the distributive property (also known as the FOIL method for binomials). Here is a step-by-step breakdown:
1. First, multiply the term $9x$ by each term in the second polynomial:
$$
9x \cdot 3x^2 = 27x^3,
$$
$$
9x \cdot 5x = 45x^2,
$$
$$
9x \cdot (-1) = -9x.
$$
So, the product of $9x$ and $(3x^2+5x-1)$ is:
$$
27x^3 + 45x^2 - 9x.
$$
2. Next, multiply the term $7$ by each term in the second polynomial:
$$
7 \cdot 3x^2 = 21x^2,
$$
$$
7 \cdot 5x = 35x,
$$
$$
7 \cdot (-1) = -7.
$$
So, the product of $7$ and $(3x^2+5x-1)$ is:
$$
21x^2 + 35x - 7.
$$
3. Now, add the two results together:
$$
(27x^3 + 45x^2 - 9x) + (21x^2 + 35x - 7).
$$
4. Combine like terms:
- The $x^3$ term: $27x^3$.
- The $x^2$ terms: $45x^2 + 21x^2 = 66x^2$.
- The $x$ terms: $-9x + 35x = 26x$.
- The constant term: $-7$.
This gives:
$$
27x^3 + 66x^2 + 26x - 7.
$$
Hence, the multiplied expression is:
$$
\boxed{27x^3 + 66x^2 + 26x - 7}.
$$
$$
(9x+7)(3x^2+5x-1),
$$
we can use the distributive property (also known as the FOIL method for binomials). Here is a step-by-step breakdown:
1. First, multiply the term $9x$ by each term in the second polynomial:
$$
9x \cdot 3x^2 = 27x^3,
$$
$$
9x \cdot 5x = 45x^2,
$$
$$
9x \cdot (-1) = -9x.
$$
So, the product of $9x$ and $(3x^2+5x-1)$ is:
$$
27x^3 + 45x^2 - 9x.
$$
2. Next, multiply the term $7$ by each term in the second polynomial:
$$
7 \cdot 3x^2 = 21x^2,
$$
$$
7 \cdot 5x = 35x,
$$
$$
7 \cdot (-1) = -7.
$$
So, the product of $7$ and $(3x^2+5x-1)$ is:
$$
21x^2 + 35x - 7.
$$
3. Now, add the two results together:
$$
(27x^3 + 45x^2 - 9x) + (21x^2 + 35x - 7).
$$
4. Combine like terms:
- The $x^3$ term: $27x^3$.
- The $x^2$ terms: $45x^2 + 21x^2 = 66x^2$.
- The $x$ terms: $-9x + 35x = 26x$.
- The constant term: $-7$.
This gives:
$$
27x^3 + 66x^2 + 26x - 7.
$$
Hence, the multiplied expression is:
$$
\boxed{27x^3 + 66x^2 + 26x - 7}.
$$
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