Question

use the chart to multiply the binomial by the trinomial.
$(2y + 3)(3y^2 + 4y + 5)$
which polynomial is the correct product?
$\circ\\ 15y^3 + 17y^2 + 22y + 15$
$\circ\\ 6y^3 + 17y^2 + 22y + 15$
$\circ\\ 6y^3 + 20y^2 + 22y + 15$
$\circ\\ 6y^3 + 17y^2 + 22y + 25$

Explanation:

Step1: Set up the grid

Label rows with $2y, 3$; columns with $3y^2, 4y, 5$.

Step2: Calculate grid entries

• $2y \times 3y^2 = 6y^3$
• $2y \times 4y = 8y^2$
• $2y \times 5 = 10y$
• $3 \times 3y^2 = 9y^2$
• $3 \times 4y = 12y$
• $3 \times 5 = 15$

Step3: Combine like terms

Combine $y^2$ terms: $8y^2 + 9y^2 = 17y^2$
Combine $y$ terms: $10y + 12y = 22y$

Step4: Assemble the polynomial

Combine all terms: $6y^3 + 17y^2 + 22y + 15$

Answer:

$\boldsymbol{6y^3 + 17y^2 + 22y + 15}$ (corresponding to the second option)