Question Simplify the expression $(6 z-i)^{2}$ as a trinomial.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $(6z - i)^2$ .
2. We need to expand this expression to write it as a trinomial.
3. We will use the formula $(a - b)^2 = a^2 - 2ab + b^2$ to expand the expression.

STEP 2

Identify the terms $a$ and $b$ in the given expression, where $a = 6z$ and $b = i$ .

STEP 3

Apply the formula $(a - b)^2 = a^2 - 2ab + b^2$ to the given expression.

STEP 4

Calculate the square of $a$ , which is $(6z)^2$ .
$a^2 = (6z)^2 = 36z^2$

STEP 5

Calculate the product of $2ab$ , which is $2 \cdot 6z \cdot i$ .
$2ab = 2 \cdot 6z \cdot i = 12zi$

STEP 6

Calculate the square of $b$ , which is $i^2$ .
$b^2 = i^2 = -1$

STEP 7

Substitute the calculated values into the expanded form.
$(6z - i)^2 = a^2 - 2ab + b^2 = 36z^2 - 12zi - 1$

STEP 8

Write the final trinomial in simplest form.
$(6z - i)^2 = 36z^2 - 12zi - 1$
This is the trinomial in its simplest form.

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