What is (3a-2b)^3+(2b-5c)^3+(5c-3a)^3 ?

The solution to (3a-2b)^3+(2b-5c)^3+(5c-3a)^3 is -54a^2b+36ab^2-60b^2c+150bc^2-225ac^2+135a^2c

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simplify (3a-2b)^3+(2b-5c)^3+(5c-3a)^3

simplify

(3 a - 2 b)^{3} + (2 b - 5 c)^{3} + (5 c - 3 a)^{3}

- 54 a^{2} b + 36 a b^{2} - 60 b^{2} c + 150 b c^{2} - 225 a c^{2} + 135 a^{2} c

Solution steps

(3 a - 2 b)^{3} + (2 b - 5 c)^{3} + (5 c - 3 a)^{3}

Expand

(3 a - 2 b)^{3} : 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3}

= 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3} + (2 b - 5 c)^{3} + (5 c - 3 a)^{3}

Expand

(2 b - 5 c)^{3} : 8 b^{3} - 60 b^{2} c + 150 b c^{2} - 125 c^{3}

= 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3} + 8 b^{3} - 60 b^{2} c + 150 b c^{2} - 125 c^{3} + (5 c - 3 a)^{3}

Expand

(5 c - 3 a)^{3} : 125 c^{3} - 225 a c^{2} + 135 a^{2} c - 27 a^{3}

= 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 8 b^{3} + 8 b^{3} - 60 b^{2} c + 150 b c^{2} - 125 c^{3} + 125 c^{3} - 225 a c^{2} + 135 a^{2} c - 27 a^{3}

Add similar elements:

- 8 b^{3} + 8 b^{3} = 0

= 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 60 b^{2} c + 150 b c^{2} - 125 c^{3} + 125 c^{3} - 225 a c^{2} + 135 a^{2} c - 27 a^{3}

Add similar elements:

- 125 c^{3} + 125 c^{3} = 0

= 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 60 b^{2} c + 150 b c^{2} - 225 a c^{2} + 135 a^{2} c - 27 a^{3}

Group like terms

= 27 a^{3} - 27 a^{3} - 54 a^{2} b + 36 a b^{2} - 60 b^{2} c + 150 b c^{2} - 225 a c^{2} + 135 a^{2} c

Add similar elements:

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

= - 54 a^{2} b + 36 a b^{2} - 60 b^{2} c + 150 b c^{2} - 225 a c^{2} + 135 a^{2} c

\frac{18 x}{6 - 12 x}

7 x^{5} - 7 x y^{2}

\frac{( 2 ^{n + 4} - 2 \cdot 2 ^{n} )}{( 2 \cdot 2 ^{n + 3} ) + 2 ^{- 3}}

(3 z - 2 y)^{3}

\frac{1 + 1}{( x + 2 ) ^{2}}

What is (3a-2b)^3+(2b-5c)^3+(5c-3a)^3 ?
The solution to (3a-2b)^3+(2b-5c)^3+(5c-3a)^3 is -54a^2b+36ab^2-60b^2c+150bc^2-225ac^2+135a^2c