What is (3x+4y)^3+(3x-4y)^3 ?

The solution to (3x+4y)^3+(3x-4y)^3 is 54x^3+288xy^2

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simplify (3x+4y)^3+(3x-4y)^3

simplify

(3 x + 4 y)^{3} + (3 x - 4 y)^{3}

54 x^{3} + 288 x y^{2}

Solution steps

(3 x + 4 y)^{3} + (3 x - 4 y)^{3}

Expand

(3 x + 4 y)^{3} : 27 x^{3} + 108 x^{2} y + 144 x y^{2} + 64 y^{3}

= 27 x^{3} + 108 x^{2} y + 144 x y^{2} + 64 y^{3} + (3 x - 4 y)^{3}

Expand

(3 x - 4 y)^{3} : 27 x^{3} - 108 x^{2} y + 144 x y^{2} - 64 y^{3}

= 27 x^{3} + 108 x^{2} y + 144 x y^{2} + 64 y^{3} + 27 x^{3} - 108 x^{2} y + 144 x y^{2} - 64 y^{3}

Group like terms

= 27 x^{3} + 27 x^{3} + 108 x^{2} y - 108 x^{2} y + 144 x y^{2} + 144 x y^{2} + 64 y^{3} - 64 y^{3}

Add similar elements:

27 x^{3} + 27 x^{3} = 54 x^{3}

= 54 x^{3} + 108 x^{2} y - 108 x^{2} y + 144 x y^{2} + 144 x y^{2} + 64 y^{3} - 64 y^{3}

Add similar elements:

108 x^{2} y - 108 x^{2} y = 0

= 54 x^{3} + 144 x y^{2} + 144 x y^{2} + 64 y^{3} - 64 y^{3}

Add similar elements:

144 x y^{2} + 144 x y^{2} = 288 x y^{2}

= 54 x^{3} + 288 x y^{2} + 64 y^{3} - 64 y^{3}

Add similar elements:

64 y^{3} - 64 y^{3} = 0

= 54 x^{3} + 288 x y^{2}

\frac{( 16 y ^{2} + 48 y )}{( 16 y )}

22 \cdot x^{3} - 33 \cdot y^{3}

s - \frac{4}{5} - \frac{3}{2} - \frac{1}{6}

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

6 (5 x + 7) - 7

What is (3x+4y)^3+(3x-4y)^3 ?
The solution to (3x+4y)^3+(3x-4y)^3 is 54x^3+288xy^2