Answer:
[tex]6y^{3}+17y^2+22y+15[/tex]
Step-by-step explanation:
We are asked to find the polynomial that is the result of the product of [tex](2y+3)(3y^2+4y+5)[/tex].
We will use distributive property [tex]a(b+c)=a*b+a*c[/tex] to solve our given problem.
[tex]2y(3y^2+4y+5)+3(3y^2+4y+5)[/tex]
[tex]2y*3y^2+2y*4y+2y*5+3*3y^2+3*4y+3*5[/tex]
We will use exponent property [tex]a^m\cdot a^n =a^{m+n}[/tex] to simplify our polynomial.
[tex]2*3y^{2+1}+2*4y^{1+1}+2y*5+3*3y^2+3*4y+3*5[/tex]
[tex]6y^{3}+8y^{2}+10y+9y^2+12y+15[/tex]
Now we will combine like terms.
[tex]6y^{3}+8y^{2}+9y^2+12y+10y+15[/tex]
[tex]6y^{3}+17y^2+22y+15[/tex]
Therefore, the polynomial [tex]6y^{3}+17y^2+22y+15[/tex] is the correct product of our given expressions.
