Question

Question was provided via image upload.

Explanation:

For \( 6x(3 + 2x) \):

Step1: Apply distributive property

Multiply \( 6x \) with each term inside the parentheses: \( 6x \times 3 + 6x \times 2x \)

Step2: Simplify each term

\( 6x \times 3 = 18x \) and \( 6x \times 2x = 12x^2 \)

Step3: Write in standard quadratic form

Arrange the terms in descending order of exponents: \( 12x^2 + 18x \)

Step1: Apply distributive property

Multiply \( 6i \) with each term inside the parentheses: \( 6i \times 3 + 6i \times 2i \)

Step2: Simplify each term

\( 6i \times 3 = 18i \) and \( 6i \times 2i = 12i^2 \)

Step3: Substitute \( i^2 = -1 \)

\( 12i^2 = 12\times(-1) = -12 \)

Step4: Combine like terms and write in standard form \( a + bi \)

\( 18i - 12 = -12 + 18i \)

Answer:

\( 12x^2 + 18x \)

For \( 6i(3 + 2i) \):