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QuestionSimplify the expression: (1−5a−8a2)−(8a+2a3−a2)(1 - 5a - 8a^2) - (8a + 2a^3 - a^2).

Studdy Solution

STEP 1

Assumptions1. We are given the expression (1−5a−8a)−(8a+a3−a)\left(1-5 a-8 a^{}\right)-\left(8 a+ a^{3}-a^{}\right). We need to simplify this expression

STEP 2

First, we need to distribute the negative sign to each term in the second parentheses.
(1−5a−8a2)−(8a+2a−a2)=1−5a−8a2−8a−2a+a2\left(1-5 a-8 a^{2}\right)-\left(8 a+2 a^{}-a^{2}\right) =1-5 a-8 a^{2} -8 a -2 a^{} + a^{2}

STEP 3

Next, we need to combine like terms. This means adding or subtracting the coefficients of the terms that have the same variable raised to the same power.
1−5a−8a2−8a−2a3+a2=1−5a−8a−8a2+a2−2a31-5 a-8 a^{2} -8 a -2 a^{3} + a^{2} =1 -5a -8a -8a^{2} + a^{2} -2a^{3}

STEP 4

Combine the like terms.
1−a−8a−8a2+a2−2a3=1−13a−7a2−2a31 -a -8a -8a^{2} + a^{2} -2a^{3} =1 -13a -7a^{2} -2a^{3}So, the simplified form of the given expression is 1−13a−7a2−2a31 -13a -7a^{2} -2a^{3}.

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