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

The correct product of \((5r - 4)(r^2 - 6r + 4)\) is:

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

This is found by expanding and combining like terms, as shown in the previous explanation.

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

1. What happens if you multiply two binomials instead of a binomial and a trinomial?
2. How do you factor a cubic polynomial like \(5r^3 - 34r^2 + 44r - 16\)?
3. Can you determine the roots of the polynomial \(r^2 - 6r + 4\) before multiplying?
4. What is the effect of a negative sign when expanding polynomial expressions?
5. How do you verify the result of polynomial multiplication?

**Tip:** When multiplying polynomials, organizing your work systematically helps ensure you don't miss any terms.

Learn how to expand and simplify the expression (5r - 4)(r^2 - 6r + 4). This problem involves the multiplication of polynomials and simplification of resulting terms. Suitable for students in Grades 9-12.

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