What is the product?

(5*r* − 4)(*r*2 − 6*r* + 4)

5*r*3 − 34*r*2 + 44*r* − 16

5*r*3 − 4*r*2 + 14*r* − 16

5*r*3 − 6*r* − 16

5*r*3 + 10*r* − 16

To find the product of the two polynomials \((5r - 4)(r^2 - 6r + 4)\), we need to expand the expression.

Let's expand it step by step:

\[
(5r - 4)(r^2 - 6r + 4)
\]

Multiply each term in the first polynomial by each term in the second polynomial:

1. \(5r \cdot r^2 = 5r^3\)
2. \(5r \cdot (-6r) = -30r^2\)
3. \(5r \cdot 4 = 20r\)
4. \(-4 \cdot r^2 = -4r^2\)
5. \(-4 \cdot (-6r) = 24r\)
6. \(-4 \cdot 4 = -16\)

Now, combine all the terms:

\[
5r^3 - 30r^2 + 20r - 4r^2 + 24r - 16
\]

Combine like terms:

\[
5r^3 - 34r^2 + 44r - 16
\]

So, the correct product is:

\[
\boxed{5r^3 - 34r^2 + 44r - 16}
\]

Would you like more details or have any questions? Here are 5 related questions:

1. How do you expand and simplify the product of two binomials?
2. What are the steps to combine like terms after expanding a polynomial expression?
3. How do you identify the degree of a polynomial?
4. What is the distributive property in polynomial multiplication?
5. How can you check if a polynomial expansion is correct?

**Tip:** Always double-check each term when expanding polynomials to avoid simple errors in sign or coefficient.

Learn how to expand and simplify the product of two polynomials (5r - 4)(r^2 - 6r + 4) step-by-step. This problem covers polynomial multiplication and combining like terms, suitable for high school students.

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