What is (-x^4+5x^2-3x-1)-(5x^4+3x^3-x^2-2x+3) ?

The solution to (-x^4+5x^2-3x-1)-(5x^4+3x^3-x^2-2x+3) is -6x^4-3x^3+6x^2-x-4

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simplify (-x^4+5x^2-3x-1)-(5x^4+3x^3-x^2-2x+3)

simplify

(- x^{4} + 5 x^{2} - 3 x - 1) - (5 x^{4} + 3 x^{3} - x^{2} - 2 x + 3)

- 6 x^{4} - 3 x^{3} + 6 x^{2} - x - 4

Solution steps

(- x^{4} + 5 x^{2} - 3 x - 1) - (5 x^{4} + 3 x^{3} - x^{2} - 2 x + 3)

Apply rule:

(a) = a

(- x^{4} + 5 x^{2} - 3 x - 1) = - x^{4} + 5 x^{2} - 3 x - 1

= - x^{4} + 5 x^{2} - 3 x - 1 - (5 x^{4} + 3 x^{3} - x^{2} - 2 x + 3)

Apply the distributive law:

- (a + b) = - a - b

- (5 x^{4} + 3 x^{3} - x^{2} - 2 x + 3) = - 5 x^{4} - 3 x^{3} + x^{2} + 2 x - 3

= - x^{4} + 5 x^{2} - 3 x - 1 - 5 x^{4} - 3 x^{3} + x^{2} + 2 x - 3

Group like terms

= - x^{4} - 5 x^{4} - 3 x^{3} + 5 x^{2} + x^{2} - 3 x + 2 x - 1 - 3

Add similar elements:

- x^{4} - 5 x^{4} = - 6 x^{4}

= - 6 x^{4} - 3 x^{3} + 5 x^{2} + x^{2} - 3 x + 2 x - 1 - 3

Add similar elements:

5 x^{2} + x^{2} = 6 x^{2}

= - 6 x^{4} - 3 x^{3} + 6 x^{2} - 3 x + 2 x - 1 - 3

Add similar elements:

- 3 x + 2 x = - x

= - 6 x^{4} - 3 x^{3} + 6 x^{2} - x - 1 - 3

Subtract the numbers:

- 1 - 3 = - 4

= - 6 x^{4} - 3 x^{3} + 6 x^{2} - x - 4

ln (e^{- 2 x})

- 28

\frac{1}{2 + 1}

(x - 2) (x + 1) (x + 5)

lo g_{3} (\frac{1}{8})

What is (-x^4+5x^2-3x-1)-(5x^4+3x^3-x^2-2x+3) ?
The solution to (-x^4+5x^2-3x-1)-(5x^4+3x^3-x^2-2x+3) is -6x^4-3x^3+6x^2-x-4