Question

use the chart to multiply the binomial by the trinomial.
$(y + 3)(y^2 - 3y + 9)$
what is the product?
$\bigcirc\\ y^3 + 27$
$\bigcirc\\ y^3 - 27$
$\bigcirc\\ y^3 - 6y^2 + 27$
$\bigcirc\\ y^3 + 6y^2 + 27$

Explanation:

Step1: Apply distributive property (FOIL for binomial-trinomial)

Multiply \( y \) with each term in \( y^2 - 3y + 9 \): \( y \cdot y^2 = y^3 \), \( y \cdot (-3y) = -3y^2 \), \( y \cdot 9 = 9y \).

Step2: Multiply 3 with each term in \( y^2 - 3y + 9 \)

\( 3 \cdot y^2 = 3y^2 \), \( 3 \cdot (-3y) = -9y \), \( 3 \cdot 9 = 27 \).

Step3: Combine like terms

Sum the results: \( y^3 - 3y^2 + 9y + 3y^2 - 9y + 27 \). The \( -3y^2 \) and \( 3y^2 \) cancel, \( 9y \) and \( -9y \) cancel, leaving \( y^3 + 27 \).

Answer:

\( y^3 + 27 \) (corresponding to the first option: \( y^3 + 27 \))