What is (x-2)^3-(x-3)(x^2+3x+9)+(x+1)^3 ?

The solution to (x-2)^3-(x-3)(x^2+3x+9)+(x+1)^3 is x^3-3x^2+15x+20

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simplify (x-2)^3-(x-3)(x^2+3x+9)+(x+1)^3

simplify

(x - 2)^{3} - (x - 3) (x^{2} + 3 x + 9) + (x + 1)^{3}

x^{3} - 3 x^{2} + 15 x + 20

Solution steps

(x - 2)^{3} - (x - 3) (x^{2} + 3 x + 9) + (x + 1)^{3}

Expand

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

= x^{3} - 6 x^{2} + 12 x - 8 - (x - 3) (x^{2} + 3 x + 9) + (x + 1)^{3}

Expand

- (x - 3) (x^{2} + 3 x + 9) : - x^{3} + 27

= x^{3} - 6 x^{2} + 12 x - 8 - x^{3} + 27 + (x + 1)^{3}

Expand

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

= x^{3} - 6 x^{2} + 12 x - 8 - x^{3} + 27 + x^{3} + 3 x^{2} + 3 x + 1

Group like terms

= x^{3} - x^{3} + x^{3} - 6 x^{2} + 3 x^{2} + 12 x + 3 x - 8 + 27 + 1

Add similar elements:

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

= x^{3} - 6 x^{2} + 3 x^{2} + 12 x + 3 x - 8 + 27 + 1

Add similar elements:

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

= x^{3} - 3 x^{2} + 12 x + 3 x - 8 + 27 + 1

Add similar elements:

12 x + 3 x = 15 x

= x^{3} - 3 x^{2} + 15 x - 8 + 27 + 1

Add the numbers:

- 8 + 27 + 1 = 20

= x^{3} - 3 x^{2} + 15 x + 20

(1 0^{x})^{y}

\frac{( x - 1 ) ( x + 1 )}{x ( x - 1 )}

12 a^{2} - 10 a

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

\frac{( 6 x )}{3}

What is (x-2)^3-(x-3)(x^2+3x+9)+(x+1)^3 ?
The solution to (x-2)^3-(x-3)(x^2+3x+9)+(x+1)^3 is x^3-3x^2+15x+20