What is (y+3)^3+(y-3)^3-54y ?

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

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simplify (y+3)^3+(y-3)^3-54y

simplify

(y + 3)^{3} + (y - 3)^{3} - 54 y

2 y^{3}

Solution steps

(y + 3)^{3} + (y - 3)^{3} - 54 y

Expand

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

= y^{3} + 9 y^{2} + 27 y + 27 + (y - 3)^{3} - 54 y

Expand

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

= y^{3} + 9 y^{2} + 27 y + 27 + y^{3} - 9 y^{2} + 27 y - 27 - 54 y

Group like terms

= y^{3} + y^{3} + 9 y^{2} - 9 y^{2} + 27 y + 27 y - 54 y + 27 - 27

Add similar elements:

y^{3} + y^{3} = 2 y^{3}

= 2 y^{3} + 9 y^{2} - 9 y^{2} + 27 y + 27 y - 54 y + 27 - 27

Add similar elements:

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

= 2 y^{3} + 27 y + 27 y - 54 y + 27 - 27

Add similar elements:

27 y + 27 y - 54 y = 0

= 2 y^{3} + 27 - 27

Subtract the numbers:

27 - 27 = 0

= 2 y^{3}

(- 6) - 3

\frac{2}{x} + \frac{3}{x}

\frac{36}{( - 4 )}

121 x^{2} y^{2} - 1