Question

find the product.
3y⁴(5y + 1)(y - 2)

3y⁴(5y + 1)(y - 2) = \square
(simplify your answer.)

Explanation:

Step1: Multiply (5y + 1)(y - 2)

Using the distributive property (FOIL method):
\((5y + 1)(y - 2) = 5y \cdot y + 5y \cdot (-2) + 1 \cdot y + 1 \cdot (-2)\)
\(= 5y^2 - 10y + y - 2\)
\(= 5y^2 - 9y - 2\)

Step2: Multiply \(3y^4\) with the result

Multiply \(3y^4\) by each term in \(5y^2 - 9y - 2\):
\(3y^4 \cdot 5y^2 = 15y^{4 + 2} = 15y^6\)
\(3y^4 \cdot (-9y) = -27y^{4 + 1} = -27y^5\)
\(3y^4 \cdot (-2) = -6y^4\)

Combine these terms:
\(15y^6 - 27y^5 - 6y^4\)

Answer:

\(15y^6 - 27y^5 - 6y^4\)