Find the product. Simplify your answer. (4b - 3)(2b^2 + 3b + 4) ______

Distribute terms: First, we need to distribute each term in the first polynomial (4b - 3) to each term in the second polynomial (2b^2 + 3b + 4). This is done by multiplying each term in the first polynomial by each term in the second polynomial.Multiply terms: Multiply 4b by each term in the second polynomial: 4b * 2b^2, 4b * 3b, and 4b * 4. This gives us: 8b^3, 12b^2, and 16b.Combine results: Now, multiply -3 by each term in the second polynomial: -3 * 2b^2, -3 * 3b, and -3 * 4. This gives us: -6b^2, -9b, and -12.Combine like terms: Combine the results from the previous steps to get the full expression: 8b^3 + 12b^2 + 16b - 6b^2 - 9b - 12.Perform subtraction: Now, we need to combine like terms. The like terms are 12b^2 and -6b^2, as well as 16b and -9b. This simplifies to: 8b^3 + (12b^2 - 6b^2) + (16b - 9b) - 12.Perform the subtraction for the like terms: 8b^3 + 6b^2 + 7b - 12.

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Algebra 1

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Q. Find the product. Simplify your answer.

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(4b - 3)(2b^2 + 3b + 4)

Distribute terms: First, we need to distribute each term in the first polynomial $(4b - 3)$ to each term in the second polynomial $(2b^2 + 3b + 4)$ . This is done by multiplying each term in the first polynomial by each term in the second polynomial.
Multiply terms: Multiply $4b$ by each term in the second polynomial: $4b \times 2b^2$ , $4b \times 3b$ , and $4b \times 4$ . This gives us: $8b^3$ , $12b^2$ , and $16b$ .
Combine results: Now, multiply $-3$ by each term in the second polynomial: $-3 \times 2b^2$ , $-3 \times 3b$ , and $-3 \times 4$ . This gives us: $-6b^2$ , $-9b$ , and $-12$ .
Combine like terms: Combine the results from the previous steps to get the full expression: $8b^3 + 12b^2 + 16b - 6b^2 - 9b - 12$ .
Perform subtraction: Now, we need to combine like terms. The like terms are $12b^2$ and $-6b^2$ , as well as $16b$ and $-9b$ . This simplifies to: $8b^3 + (12b^2 - 6b^2) + (16b - 9b) - 12$ .
Perform subtraction: Now, we need to combine like terms. The like terms are $12b^2$ and $-6b^2$ , as well as $16b$ and $-9b$ . This simplifies to: $8b^3 + (12b^2 - 6b^2) + (16b - 9b) - 12$ . Perform the subtraction for the like terms: $8b^3 + 6b^2 + 7b - 12$ .