What is (2x+3y)^3-(x^3+27y^3) ?

The solution to (2x+3y)^3-(x^3+27y^3) is 7x^3+36x^2y+54xy^2

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simplify (2x+3y)^3-(x^3+27y^3)

simplify

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

7 x^{3} + 36 x^{2} y + 54 x y^{2}

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

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

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

Group like terms

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

Add similar elements:

8 x^{3} - x^{3} = 7 x^{3}

= 7 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} - 27 y^{3}

Add similar elements:

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

= 7 x^{3} + 36 x^{2} y + 54 x y^{2}

\frac{x ^{2} - 3 x}{2 - 7}

5^{y} + 5^{y + 1}

(a^{- 1} + b^{- 1}) (a + b)^{- 1}

\frac{4.5 x 1 0 ^{- 2}}{8.3 x 1 0 ^{4}}

(x + a) (x - a) (x^{2} + a^{2}) (x^{4} + a^{4}) + a^{8}

What is (2x+3y)^3-(x^3+27y^3) ?
The solution to (2x+3y)^3-(x^3+27y^3) is 7x^3+36x^2y+54xy^2