what is the product?\n(5r - 4)(r² - 6r + 4)\n○ 5r³ - 34r² + 44r - 16\n○ 5r³ - 4r² + 14r - 16\n○ 5r³ - 6r…

Explanation:

Step1: Use distributive property

[ \begin{align*} &(5r - 4)(r^{2}-6r + 4)\ =&5r\times(r^{2}-6r + 4)-4\times(r^{2}-6r + 4) \end{align*} ]

Step2: Multiply each term

[ \begin{align*} 5r\times(r^{2}-6r + 4)&=5r\times r^{2}-5r\times6r+5r\times4\ &=5r^{3}-30r^{2}+20r \end{align*} ] [ \begin{align*} -4\times(r^{2}-6r + 4)&=-4\times r^{2}+(-4)\times(-6r)+(-4)\times4\ &=-4r^{2}+24r - 16 \end{align*} ]

Step3: Combine like - terms

[ \begin{align*} &(5r^{3}-30r^{2}+20r)+(-4r^{2}+24r - 16)\ =&5r^{3}+(-30r^{2}-4r^{2})+(20r + 24r)-16\ =&5r^{3}-34r^{2}+44r - 16 \end{align*} ]

Answer:

A. (5r^{3}-34r^{2}+44r - 16)