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

The solution to (2x+3y)^3+(2x-3y)^3 is 16x^3+108xy^2

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

simplify

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

16 x^{3} + 108 x y^{2}

Solution steps

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

Expand

(2 x + 3 y)^{3} : 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}

= 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} + (2 x - 3 y)^{3}

Expand

(2 x - 3 y)^{3} : 8 x^{3} - 36 x^{2} y + 54 x y^{2} - 27 y^{3}

= 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} + 8 x^{3} - 36 x^{2} y + 54 x y^{2} - 27 y^{3}

Group like terms

= 8 x^{3} + 8 x^{3} + 36 x^{2} y - 36 x^{2} y + 54 x y^{2} + 54 x y^{2} + 27 y^{3} - 27 y^{3}

Add similar elements:

8 x^{3} + 8 x^{3} = 16 x^{3}

= 16 x^{3} + 36 x^{2} y - 36 x^{2} y + 54 x y^{2} + 54 x y^{2} + 27 y^{3} - 27 y^{3}

Add similar elements:

36 x^{2} y - 36 x^{2} y = 0

= 16 x^{3} + 54 x y^{2} + 54 x y^{2} + 27 y^{3} - 27 y^{3}

Add similar elements:

54 x y^{2} + 54 x y^{2} = 108 x y^{2}

= 16 x^{3} + 108 x y^{2} + 27 y^{3} - 27 y^{3}

Add similar elements:

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

= 16 x^{3} + 108 x y^{2}

81 x^{2} - 144 y^{2}

8^{3} + 8 (x - y)^{3}

x^{15} + 15 x y

\frac{( 7 x ^{6} - 8 x ^{5} \cdot y + x ^{4} \cdot y ^{3} )}{( \frac{1}{2} \cdot x ^{3} )}

(3 x - 5 y)^{3} + (3 x - 5 y)^{3}

What is (2x+3y)^3+(2x-3y)^3 ?
The solution to (2x+3y)^3+(2x-3y)^3 is 16x^3+108xy^2