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

The solution to (x+3)(x^2-3x+9)-(x-1)^3+3(x^2-1) is 6x^2-3x+25

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

simplify

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

6 x^{2} - 3 x + 25

Solution steps

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

Expand

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

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

Add the numbers:

27 + 1 - 3 = 25

= 6 x^{2} - 3 x + 25

3 x^{2} + 13 x y - 10 y^{2}

a [13] + a [20] - a [23]

\frac{2}{5} + \frac{1}{4} + \frac{1}{3} - \frac{1}{x}

(x + 2) (x - 12)

(0.5 a)^{3} (0.5 a)^{- 2}

What is (x+3)(x^2-3x+9)-(x-1)^3+3(x^2-1) ?
The solution to (x+3)(x^2-3x+9)-(x-1)^3+3(x^2-1) is 6x^2-3x+25