Which expression is the product of (4x + 3) and (x2 + 7x − 2)

To find the product of the expressions \((4x + 3)\) and \((x^2 + 7x - 2)\), we need to distribute each term in the first expression to each term in the second expression.

Here’s the step-by-step process:

1. Distribute \(4x\) to each term in \(x^2 + 7x - 2\):
\[4x \cdot x^2 + 4x \cdot 7x + 4x \cdot (-2)\]
\[= 4x^3 + 28x^2 - 8x\]

2. Distribute \(3\) to each term in \(x^2 + 7x - 2\):
\[3 \cdot x^2 + 3 \cdot 7x + 3 \cdot (-2)\]
\[= 3x^2 + 21x - 6\]

3. Combine all the terms together:
\[4x^3 + 28x^2 - 8x + 3x^2 + 21x - 6\]

4. Combine like terms:
\[4x^3 + (28x^2 + 3x^2) + (-8x + 21x) - 6\]
\[= 4x^3 + 31x^2 + 13x - 6\]

So, the product of \((4x + 3)\) and \((x^2 + 7x - 2)\) is:

\[4x^3 + 31x^2 + 13x - 6\]

Would you like more details or have any questions? Here are some questions you might want to ask:

1. How do you factor polynomial expressions?
2. Can you explain the distributive property in algebra?
3. What are like terms and how do you combine them?
4. How do you solve quadratic equations?
5. What is the difference between polynomial and rational expressions?

Tip: When multiplying polynomials, always ensure to distribute each term in the first polynomial to every term in the second polynomial to avoid missing any terms.

Learn how to find the product of (4x + 3) and (x^2 + 7x - 2) using the distributive property with a detailed step-by-step solution. This problem involves polynomial multiplication and is suitable for Grades 7-9 students.

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