Question

multiply.
(2 - 3a)(5 + 6a)
simplify your answer.

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
\( (2 - 3a)(5 + 6a) = 2\times5 + 2\times6a - 3a\times5 - 3a\times6a \)

Step2: Simplify each product

Calculate each term:
\( 2\times5 = 10 \), \( 2\times6a = 12a \), \( -3a\times5 = -15a \), \( -3a\times6a = -18a^2 \)

Step3: Combine like terms

Combine the \( 12a \) and \( -15a \) terms:
\( 10 + (12a - 15a) - 18a^2 = 10 - 3a - 18a^2 \)

Step4: Rearrange the terms (optional, but standard form is preferred)

Write the polynomial in standard form (descending powers of \( a \)):
\( -18a^2 - 3a + 10 \) or \( 10 - 3a - 18a^2 \) (both are correct, but standard form is usually with the highest degree first)

Answer:

\( -18a^2 - 3a + 10 \) (or \( 10 - 3a - 18a^2 \))