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

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

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

simplify

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

54 x^{2} y + 2 y^{3}

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

27 x^{3} - 27 x^{3} = 0

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

Add similar elements:

27 x^{2} y + 27 x^{2} y = 54 x^{2} y

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

Add similar elements:

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

= 54 x^{2} y + y^{3} + y^{3}

Add similar elements:

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

= 54 x^{2} y + 2 y^{3}

5 \frac{a ^{3}}{18} b^{3}

49 c^{2} - (a^{b})^{4}

(3 q + 2)^{3}

((x^{2})^{x})^{2}

\frac{1}{a + b}