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QuestionSimplify the expression: (−1−4x3−12x2)−(11+13x3+6x2)(-1 - 4x^3 - 12x^2) - (11 + 13x^3 + 6x^2).

Studdy Solution

STEP 1

Assumptions1. We are given two polynomial expressions −1−4x3−12x-1-4 x^{3}-12 x^{} and 11+13x3+6x11+13 x^{3}+6 x^{}. . We are asked to find the difference between these two expressions.

STEP 2

To find the difference between two expressions, we subtract the second expression from the first.Difference=(−1−4x−12x2)−(11+13x+6x2)Difference = \left(-1-4 x^{}-12 x^{2}\right)-\left(11+13 x^{}+6 x^{2}\right)

STEP 3

To subtract the second expression from the first, we distribute the negative sign to each term in the second expression.Difference=−1−x3−12x2−11−13x3−6x2Difference = -1- x^{3}-12 x^{2} -11 -13 x^{3} -6 x^{2}

STEP 4

Now, we can combine like terms.Difference=−1−11−4x3−13x3−12x2−6x2Difference = -1 -11 -4x^{3} -13x^{3} -12x^{2} -6x^{2}

STEP 5

Combine the constant terms (-1 and -11), the x3x^{3} terms (-4x^{3} and -13x^{3}), and the x2x^{2} terms (-12x^{2} and -x^{2}).
Difference=−1−11−4x3−13x3−12x2−x2=−12−17x3−18x2Difference = -1 -11 -4x^{3} -13x^{3} -12x^{2} -x^{2} = -12 -17x^{3} -18x^{2}So, the simplified difference of the given expressions is −17x3−18x2−12-17 x^{3}-18 x^{2}-12.

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