Math

QuestionSimplify the expression: (2a4+a3+4)(58a3+a4)(2 a^{4}+a^{3}+4)-(5-8 a^{3}+a^{4}).

Studdy Solution

STEP 1

Assumptions1. The given expression is (a4+a3+4)(58a3+a4)\left( a^{4}+a^{3}+4\right)-\left(5-8 a^{3}+a^{4}\right). We are assuming that aa is a real number.

STEP 2

We need to simplify the given expression. The first step is to remove the parentheses. Remember that when we remove parentheses, we need to distribute the negative sign to each term in the second parentheses.
(2a4+a+4)(58a+a4)=2a4+a+45+8aa4\left(2 a^{4}+a^{}+4\right)-\left(5-8 a^{}+a^{4}\right) =2 a^{4}+a^{}+4 -5 +8 a^{} - a^{4}

STEP 3

Next, we need to combine like terms. Like terms are those terms which have the same variable and exponent. In this case, 2a2 a^{} and a- a^{} are like terms, a3a^{3} and 8a38 a^{3} are like terms, and $$ and $-5$ are like terms.
2a+a3+5+8a3a=(2aa)+(a3+8a3)+(5)2 a^{}+a^{3}+ -5 +8 a^{3} - a^{} = (2 a^{} - a^{}) + (a^{3} +8 a^{3}) + ( -5)

STEP 4

Now, perform the operations to simplify each of the grouped terms.
(2a4a4)+(a3+8a3)+(4)=a4+9a31(2 a^{4} - a^{4}) + (a^{3} +8 a^{3}) + (4 -) = a^{4} +9 a^{3} -1So, the simplified form of the given expression is a4+9a31a^{4} +9 a^{3} -1.

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