QuestionSimplify the expression: $(x^{3}-4 x^{2}-5 x)-(2 x^{3}+7 x^{2}+2 x)$ .

Studdy Solution

STEP 1

Assumptions1. We are given two polynomials $x^{3}-4 x^{}-5 x$ and $x^{3}+7 x^{}+ x$ . . We are asked to subtract the second polynomial from the first.

STEP 2

We will subtract the second polynomial from the first by subtracting the corresponding terms in each polynomial.
$\left(x^{}-4 x^{2}-5 x\right)-\left(2 x^{}+7 x^{2}+2 x\right) = x^{}-4 x^{2}-5 x -2 x^{}-7 x^{2}-2 x$

STEP 3

Now we will combine like terms. $= (x^{3} -2 x^{3}) + (- x^{2} -7 x^{2}) + (-5 x -2 x)$

STEP 4

Now we will perform the subtraction for each set of like terms.
$= -x^{3} -11x^{2} -7x$ So, $\left(x^{3}-4 x^{2}- x\right)-\left(2 x^{3}+7 x^{2}+2 x\right) = -x^{3} -11x^{2} -7x$ .

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