Math

QuestionSimplify the expression: (3b4+2b3+6b)+(8b27b43b)(3 b^{4}+2 b^{3}+6 b)+(8 b^{2}-7 b^{4}-3 b).

Studdy Solution

STEP 1

Assumptions1. The given expression is (3b4+b3+6b)+(8b7b43b)\left(3 b^{4}+ b^{3}+6 b\right)+\left(8 b^{}-7 b^{4}-3 b\right). We are to simplify the expression by combining like terms.

STEP 2

First, we need to remove the parentheses. Since there is no negative sign in front of either parentheses, we can simply drop the parentheses.
b4+2b+6b+8b27b4b b^{4}+2 b^{}+6 b+8 b^{2}-7 b^{4}- b

STEP 3

Next, we rearrange the terms so that like terms are together. This means putting all bb^{} terms together, all b3b^{3} terms together, all b2b^{2} terms together, and all bb terms together.
3b7b+2b3+8b2+6b3b3 b^{}-7 b^{}+2 b^{3}+8 b^{2}+6 b-3 b

STEP 4

Now, we combine the like terms.(3b47b4)+2b3+8b2+(6b3b)\left(3 b^{4}-7 b^{4}\right)+2 b^{3}+8 b^{2}+\left(6 b-3 b\right)

STEP 5

Perform the subtraction for the b4b^{4} terms and the bb terms.
4b4+2b3+8b2+3b-4 b^{4}+2 b^{3}+8 b^{2}+3 bSo, the simplified form of the given expression is 4b4+2b3+8b2+3b-4 b^{4}+2 b^{3}+8 b^{2}+3 b.

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