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

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

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

simplify

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

x^{3} + y^{3}

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

x^{3} + 4 x^{2} + 4 x + 1

121 a^{2} - 144 b^{2}

\frac{c \cdot ( 75 )}{( 1 0 ^{- 4} )}

\frac{( x ^{2} - 2 x y + y ^{2} )}{( x - y )}

\frac{5.78}{3.2 x ^{6.1}}