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

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

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

simplify

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

- x^{3} - 6 x^{2} - 3 x + \frac{1}{2} x^{4} - 1

Solution steps

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

Expand

- (x + 1)^{3} : - x^{3} - 3 x^{2} - 3 x - 1

= \frac{1}{2} x^{4} - x^{3} - 3 x^{2} - 3 x - 1 - 3 x^{2}

Group like terms

= - x^{3} - 3 x^{2} - 3 x^{2} - 3 x + \frac{1}{2} x^{4} - 1

Add similar elements:

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

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

(sin (x) + cos (x))^{2}

(sin (t) + cos (t))^{2}

sec^{2} (x) - tan^{2} (x)

(- 1 - i 3)^{- 4}

1 + cot^{2} (x)

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