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

The solution to (x+3)^3+(x-3)^3-2x^3 is 54x

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

simplify

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

54 x

Solution steps

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

Expand

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

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

Expand

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

= x^{3} + 9 x^{2} + 27 x + 27 + x^{3} - 9 x^{2} + 27 x - 27 - 2 x^{3}

Group like terms

= x^{3} + x^{3} - 2 x^{3} + 9 x^{2} - 9 x^{2} + 27 x + 27 x + 27 - 27

Add similar elements:

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

= 9 x^{2} - 9 x^{2} + 27 x + 27 x + 27 - 27

Add similar elements:

9 x^{2} - 9 x^{2} = 0

= 27 x + 27 x + 27 - 27

Add similar elements:

27 x + 27 x = 54 x

= 54 x + 27 - 27

Subtract the numbers:

27 - 27 = 0

= 54 x

(3)^{2}

5 x + 4 \cdot 3 x + 3 x

\frac{4}{7} + \frac{- 1}{3}

y^{- 9} \cdot y^{3}

(x + y) (x + 2 y)