What is (x+2)^3+(x-3)^2-x^2*(x+5) ?

The solution to (x+2)^3+(x-3)^2-x^2*(x+5) is 2x^2+6x+17

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simplify (x+2)^3+(x-3)^2-x^2*(x+5)

simplify

(x + 2)^{3} + (x - 3)^{2} - x^{2} \cdot (x + 5)

2 x^{2} + 6 x + 17

Solution steps

(x + 2)^{3} + (x - 3)^{2} - x^{2} (x + 5)

Expand

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

= x^{3} + 6 x^{2} + 12 x + 8 + (x - 3)^{2} - x^{2} (x + 5)

Expand

(x - 3)^{2} : x^{2} - 6 x + 9

= x^{3} + 6 x^{2} + 12 x + 8 + x^{2} - 6 x + 9 - x^{2} (x + 5)

Expand

- x^{2} (x + 5) : - x^{3} - 5 x^{2}

= x^{3} + 6 x^{2} + 12 x + 8 + x^{2} - 6 x + 9 - x^{3} - 5 x^{2}

Group like terms

= x^{3} - x^{3} + 6 x^{2} + x^{2} - 5 x^{2} + 12 x - 6 x + 8 + 9

Add similar elements:

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

= 6 x^{2} + x^{2} - 5 x^{2} + 12 x - 6 x + 8 + 9

Add similar elements:

6 x^{2} + x^{2} - 5 x^{2} = 2 x^{2}

= 2 x^{2} + 12 x - 6 x + 8 + 9

Add similar elements:

12 x - 6 x = 6 x

= 2 x^{2} + 6 x + 8 + 9

Add the numbers:

8 + 9 = 17

= 2 x^{2} + 6 x + 17

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\frac{( 17 x ^{6} - x ^{6} )}{( 2 x ^{3} ) - ( 2 x ) ^{2} \cdot 2 x}

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What is (x+2)^3+(x-3)^2-x^2*(x+5) ?
The solution to (x+2)^3+(x-3)^2-x^2*(x+5) is 2x^2+6x+17