Question

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

Answer 1

Multiply each term of the binomial by each term of the trinomial:

2y*(3y^2 + 4y + 5) = 6y^3 + 8y^2 + 10y
3*(3y^2 + 4y + 5) = 9y^2 + 12y + 15

Add like terms: 6y^3 + (8+9)y^2 + (10+12)y + 15 = 6y^3 + 17y^2 + 22y + 15.