Math

QuestionSimplify the expression: (6+5m28m4)(6+5m2+7m4)(6+5 m^{2}-8 m^{4}) - (6+5 m^{2}+7 m^{4}).

Studdy Solution

STEP 1

Assumptions1. We are given two polynomial expressions, (6+5m8m4)\left(6+5 m^{}-8 m^{4}\right) and (6+5m+7m4)\left(6+5 m^{}+7 m^{4}\right). . We are asked to subtract the second polynomial from the first one.

STEP 2

To subtract one polynomial from another, we subtract the corresponding terms in the two polynomials. The corresponding terms are those that have the same power of the variable.
(6+5m28m4)(6+5m2+7m4)=(66)+(5m25m2)+(8m47m4)\left(6+5 m^{2}-8 m^{4}\right)-\left(6+5 m^{2}+7 m^{4}\right) = (6-6) + (5m^2 -5m^2) + (-8m^4 -7m^4)

STEP 3

Now, perform the subtraction for each pair of corresponding terms.
(66)+(5m25m2)+(8m7m)=0+0m2+(15m)(6-6) + (5m^2 -5m^2) + (-8m^ -7m^) =0 +0m^2 + (-15m^)

STEP 4

implify the expression to get the final result. As the first two terms are zero, they can be omitted.
0+0m2+(15m4)=15m40 +0m^2 + (-15m^4) = -15m^4So, (6+m28m4)(6+m2+7m4)=15m4\left(6+ m^{2}-8 m^{4}\right)-\left(6+ m^{2}+7 m^{4}\right) = -15m^4.

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