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

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

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

simplify

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

1

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

x^{3} - x^{3} = 0

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

Add similar elements:

3 x^{2} - 3 x^{2} = 0

= 3 x - 3 x + 1

Add similar elements:

3 x - 3 x = 0

= 1

8 x y (3 x - y + 2 z)

\frac{907}{495} + 1432323232

\frac{x ^{2} - 2 x}{x ^{2} - 4 x + 4}

(- 5 - 5 i) - (- 3 + 6 i)