Question

Which polynomial is the correct product? (2y+3)(3y2+4y+5)

Answer 1

(2y+3)(3(y^2)+4y+5)
(2y)(3(y^2))+(2y(4y))+(2y)(5)+(3(3)(y^2))+(3)(4y)+(3)(5)
6(y^3)+8(y^2)+10y+9(y^2)+12y+15
6(y^3)+17(y^2)+22y+15

Answer 2

Answer:

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

Step-by-step explanation:

We are asked to find the polynomial that is the result of the product of $(2y+3)(3y^2+4y+5)$.

We will use distributive property $a(b+c)=a*b+a*c$ to solve our given problem.

$2y(3y^2+4y+5)+3(3y^2+4y+5)$

$2y*3y^2+2y*4y+2y*5+3*3y^2+3*4y+3*5$

We will use exponent property $a^m\cdot a^n =a^{m+n}$ to simplify our polynomial.

$2*3y^{2+1}+2*4y^{1+1}+2y*5+3*3y^2+3*4y+3*5$

$6y^{3}+8y^{2}+10y+9y^2+12y+15$

Now we will combine like terms.

$6y^{3}+8y^{2}+9y^2+12y+10y+15$

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

Therefore, the polynomial $6y^{3}+17y^2+22y+15$ is the correct product of our given expressions.