Questions: Select the simplified, expanded form of the following expressions. (4 t^4 - 8 t + 4) - (8 t^2 + 4 t^4 + 1) -8 t^2 - 8 t + 3 -4 t^2 - 8 t + 3 8 t^2 - 8 t + 3 -4 t^2 - 4 t + 3

Transcript text: Select the simplified, expanded form of the following expressions. \[ \left(4 t^{4}-8 t+4\right)-\left(8 t^{2}+4 t^{4}+1\right) \] $-8 t^{2}-8 t+3$ $-4 t^{2}-8 t+3$ $8 t^{2}-8 t+3$ $-4 t^{2}-4 t+3$

Solution

Solution Steps

To simplify the given expression, we need to distribute the negative sign across the terms in the second polynomial and then combine like terms. This involves subtracting the coefficients of terms with the same degree.

Step 1: Distributing the Negative Sign

We start with the expression: \[ (4t^{4} - 8t + 4) - (8t^{2} + 4t^{4} + 1) \] Distributing the negative sign across the second polynomial gives us: \[ 4t^{4} - 8t + 4 - 8t^{2} - 4t^{4} - 1 \]

Step 2: Combining Like Terms

Next, we combine the like terms: