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

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.

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

Next, we combine the like terms:

• The $t^{4}$ terms: $4t^{4} - 4t^{4} = 0$
• The $t^{2}$ terms: $-8t^{2}$
• The $t$ terms: $-8t$
• The constant terms: $4 - 1 = 3$

Thus, the expression simplifies to: $$-8t^{2} - 8t + 3$$

Final Answer