use the chart to multiply the binomial by the trinomial. which polynomial is the correct product? (2y +…

Explanation:

Step1: Multiply each term of binomial by trinomial

$(2y + 3)(3y^{2}+4y + 5)=2y(3y^{2}+4y + 5)+3(3y^{2}+4y + 5)$

Step2: Distribute $2y$

$2y(3y^{2}+4y + 5)=2y\times3y^{2}+2y\times4y+2y\times5 = 6y^{3}+8y^{2}+10y$

Step3: Distribute $3$

$3(3y^{2}+4y + 5)=3\times3y^{2}+3\times4y+3\times5=9y^{2}+12y + 15$

Step4: Combine like - terms

$(6y^{3}+8y^{2}+10y)+(9y^{2}+12y + 15)=6y^{3}+(8y^{2}+9y^{2})+(10y + 12y)+15=6y^{3}+17y^{2}+22y + 15$

Answer:

$6y^{3}+17y^{2}+22y + 15$