what is the product?\n$(y^{2}+3y + 7)(8y^{2}+y + 1)$\n$8y^{4}+24y^{3}+60y^{2}+10y + 7$\n$8y^{4}+25y^{3}+4y^{2…

what is the product?\n$(y^{2}+3y + 7)(8y^{2}+y + 1)$\n$8y^{4}+24y^{3}+60y^{2}+10y + 7$\n$8y^{4}+25y^{3}+4y^{2}+10y + 7$\n$8y^{4}+25y^{3}+60y^{2}+7y + 7$\n$8y^{4}+25y^{3}+60y^{2}+10y + 7$

what is the product?\n$(y^{2}+3y + 7)(8y^{2}+y + 1)$\n$8y^{4}+24y^{3}+60y^{2}+10y + 7$\n$8y^{4}+25y^{3}+4y^{2}+10y + 7$\n$8y^{4}+25y^{3}+60y^{2}+7y + 7$\n$8y^{4}+25y^{3}+60y^{2}+10y + 7$

Answer

Explanation:

Step1: Use distributive property

[ \begin{align*} &(y^{2}+3y + 7)(8y^{2}+y+1)\ =&y^{2}(8y^{2}+y + 1)+3y(8y^{2}+y+1)+7(8y^{2}+y+1) \end{align*} ]

Step2: Multiply each term

For (y^{2}(8y^{2}+y + 1)): (y^{2}\times8y^{2}+y^{2}\times y+y^{2}\times1 = 8y^{4}+y^{3}+y^{2}) For (3y(8y^{2}+y+1)): (3y\times8y^{2}+3y\times y+3y\times1=24y^{3}+3y^{2}+3y) For (7(8y^{2}+y+1)): (7\times8y^{2}+7\times y+7\times1 = 56y^{2}+7y+7)

Step3: Combine like - terms

[ \begin{align*} &(8y^{4}+y^{3}+y^{2})+(24y^{3}+3y^{2}+3y)+(56y^{2}+7y+7)\ =&8y^{4}+(y^{3}+24y^{3})+(y^{2}+3y^{2}+56y^{2})+(3y + 7y)+7\ =&8y^{4}+25y^{3}+60y^{2}+10y+7 \end{align*} ]

Answer:

D. (8y^{4}+25y^{3}+60y^{2}+10y + 7)