Question

what is the product? (4y - 3)(2y² + 3y - 5) \\(\circ\\) 8y³ + 3y + 15 \\(\circ\\) 8y³ - 23y + 15 \\(\circ\\) 8y³ - 6y² - 17y + 15 \\(\circ\\) 8y³ + 6y² - 29y + 15

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second trinomial:
\(4y \times 2y^2 = 8y^3\), \(4y \times 3y = 12y^2\), \(4y \times (-5) = -20y\)
\(-3 \times 2y^2 = -6y^2\), \(-3 \times 3y = -9y\), \(-3 \times (-5) = 15\)

Step2: Combine like terms

Combine the \(y^2\) terms: \(12y^2 - 6y^2 = 6y^2\)
Combine the \(y\) terms: \(-20y - 9y = -29y\)

Step3: Write the final polynomial

Putting it all together: \(8y^3 + 6y^2 - 29y + 15\)

Answer:

\(8y^3 + 6y^2 - 29y + 15\) (the last option)