Question

multiplying polynomials and simplifying expressions
what is the product?
$(4y - 3)(2y^2 + 3y - 5)$
$8y^3 + 6y^2 - 29y + 15$
$8y^3 - 6y^2 - 17y + 15$
$8y^3 + 3y + 15$
$8y^3 - 23y + 15$

Explanation:

Step1: Distribute \(4y\)

Multiply \(4y\) by each term in \(2y^2 + 3y - 5\):
\(4y \cdot 2y^2 = 8y^3\), \(4y \cdot 3y = 12y^2\), \(4y \cdot (-5) = -20y\).

Step2: Distribute \(-3\)

Multiply \(-3\) by each term in \(2y^2 + 3y - 5\):
\(-3 \cdot 2y^2 = -6y^2\), \(-3 \cdot 3y = -9y\), \(-3 \cdot (-5) = 15\).

Step3: Combine like terms

Add the results from Step1 and Step2:
\(8y^3 + 12y^2 - 20y - 6y^2 - 9y + 15\)
Combine \(12y^2 - 6y^2 = 6y^2\) and \(-20y - 9y = -29y\):
\(8y^3 + 6y^2 - 29y + 15\).

Answer:

\(8y^3 + 6y^2 - 29y + 15\) (corresponding to the first option)