QuestionSimplify the expression: $(4 x^{2}+7 x-4 x^{4})-(6 x^{4}-5 x+1)$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $\left(4 x^{}+7 x-4 x^{4}\right)-\left(6 x^{4}-5 x+1\right)$ . We are to simplify this expression by combining like terms.

STEP 2

First, we need to distribute the negative sign to each term in the second parentheses.
$=4 x^{2}+7 x-4 x^{4} - (6 x^{4}-5 x+1)$ $=4 x^{2}+7 x-4 x^{4} -6 x^{4} +5 x -1$

STEP 3

Next, we need to combine like terms. We start with the $x^{}$ terms.
$= - x^{} -6 x^{} + x^{2} +7 x +5 x -1$ $= -10 x^{} + x^{2} +7 x +5 x -1$

STEP 4

Then we combine the $x$ terms.
$= -10 x^{4} +4 x^{2} +12 x -1$ So, the simplified expression is $-10 x^{4} +4 x^{2} +12 x -1$ .

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