To multiply the binomial (2y + 3) by the trinomial (3y^2 + 4y + 5), we distribute each term in the binomial to each term in the trinomial and then add the like terms.
When we multiply (2y) by (3y^2 + 4y + 5), we get:
6y^3 + 8y^2 + 10y
When we multiply (3) by (3y^2 + 4y + 5), we get:
9y^2 + 12y + 15
Now we add these products together:
6y^3 + 8y^2 + 10y + 9y^2 + 12y + 15 = 6y^3 + 17y^2 + 22y + 15
Therefore, the correct product is:
6y^3 + 17y^2 + 22y + 15
So the first option: 15y^3 + 17y^2 + 22y + 15 is the correct product.
Use the chart to multiply the binomial by the trinomial.
The expression (2 y + 3)(3 y squared + 4 y + 5) is shown above a blank table with 3 columns and 2 rows.
Which polynomial is the correct product?
15y3 + 17y2 + 22y + 15
6y3 + 17y2 + 22y + 15
6y3 + 20y2 + 22y + 15
6y3 + 17y2 + 22y + 25
1 answer