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

The solution to (x-2)(x+2)(x+3)-(x+1)^3 is -7x-13

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

simplify

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

- 7 x - 13

Solution steps

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

Expand

(x - 2) (x + 2) (x + 3) : x^{3} + 3 x^{2} - 4 x - 12

= x^{3} + 3 x^{2} - 4 x - 12 - (x + 1)^{3}

Expand

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

= x^{3} + 3 x^{2} - 4 x - 12 - x^{3} - 3 x^{2} - 3 x - 1

Group like terms

= x^{3} - x^{3} + 3 x^{2} - 3 x^{2} - 4 x - 3 x - 12 - 1

Add similar elements:

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

= 3 x^{2} - 3 x^{2} - 4 x - 3 x - 12 - 1

Add similar elements:

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

= - 4 x - 3 x - 12 - 1

Add similar elements:

- 4 x - 3 x = - 7 x

= - 7 x - 12 - 1

Subtract the numbers:

- 12 - 1 = - 13

= - 7 x - 13

15 (x - 3 y) - 3 \cdot (3 x - x)^{2}

16 a^{2} - 9 x^{2} y^{2}

(- 3 a^{3})^{4}

(25 - x)^{3}

(m - 3)^{4}

What is (x-2)(x+2)(x+3)-(x+1)^3 ?
The solution to (x-2)(x+2)(x+3)-(x+1)^3 is -7x-13