What is (6x-y)^3-(6x+y)^3 ?

The solution to (6x-y)^3-(6x+y)^3 is -216x^2y-2y^3

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simplify (6x-y)^3-(6x+y)^3

simplify

(6 x - y)^{3} - (6 x + y)^{3}

- 216 x^{2} y - 2 y^{3}

Solution steps

(6 x - y)^{3} - (6 x + y)^{3}

Expand

(6 x - y)^{3} : 216 x^{3} - 108 x^{2} y + 18 x y^{2} - y^{3}

= 216 x^{3} - 108 x^{2} y + 18 x y^{2} - y^{3} - (6 x + y)^{3}

Expand

- (6 x + y)^{3} : - 216 x^{3} - 108 x^{2} y - 18 x y^{2} - y^{3}

= 216 x^{3} - 108 x^{2} y + 18 x y^{2} - y^{3} - 216 x^{3} - 108 x^{2} y - 18 x y^{2} - y^{3}

Group like terms

= 216 x^{3} - 216 x^{3} - 108 x^{2} y - 108 x^{2} y + 18 x y^{2} - 18 x y^{2} - y^{3} - y^{3}

Add similar elements:

216 x^{3} - 216 x^{3} = 0

= - 108 x^{2} y - 108 x^{2} y + 18 x y^{2} - 18 x y^{2} - y^{3} - y^{3}

Add similar elements:

- 108 x^{2} y - 108 x^{2} y = - 216 x^{2} y

= - 216 x^{2} y + 18 x y^{2} - 18 x y^{2} - y^{3} - y^{3}

Add similar elements:

18 x y^{2} - 18 x y^{2} = 0

= - 216 x^{2} y - y^{3} - y^{3}

Add similar elements:

- y^{3} - y^{3} = - 2 y^{3}

= - 216 x^{2} y - 2 y^{3}

5 (a + b)

\frac{( p \cdot x ^{p - 1} )}{( q \cdot ( x ^{\frac{p}{q}} ) ^{q - 1} )}

\frac{( 6 a ^{4} + 3 a ^{3} + 6 a ^{2} )}{( 3 a ^{2} )}

(x - y + z)^{2} + 2 (x - y + z) (y - z + x) + (y - z + x)^{2}

\frac{( 9 a ^{9} - 9 a ^{7} + 18 a ^{4} )}{( 15 a ^{8} )}