question
written as a simplified polynomial in standard form, what is the result when $(2t - 1)^2$ is subtracted from $t^3$?
answer

Question

Accepted Answer

# Explanation:
## Step1: Expand $(2t - 1)^3$
Using the formula $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$, where $a = 2t$ and $b = 1$.
$$
\begin{align*}
(2t - 1)^3&=(2t)^3 - 3(2t)^2(1) + 3(2t)(1)^2 - 1^3\
&=8t^3 - 12t^2 + 6t - 1
\end{align*}
$$
## Step2: Subtract $(2t - 1)^3$ from $t^3$
The expression is $t^3 - (8t^3 - 12t^2 + 6t - 1)$.
$$
\begin{align*}
t^3 - 8t^3 + 12t^2 - 6t + 1&=(1 - 8)t^3 + 12t^2 - 6t + 1\
&=-7t^3 + 12t^2 - 6t + 1
\end{align*}
$$
# Answer:
$-7t^3 + 12t^2 - 6t + 1$

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QUESTION IMAGE

Question

Explanation:

Step1: Expand \((2t - 1)^3\)

Step2: Subtract \((2t - 1)^3\) from \(t^3\)

Answer: