What is (2p+q)^3-(p+2q)^3 ?

The solution to (2p+q)^3-(p+2q)^3 is 7p^3+6p^2q-6pq^2-7q^3

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simplify (2p+q)^3-(p+2q)^3

simplify

(2 p + q)^{3} - (p + 2 q)^{3}

7 p^{3} + 6 p^{2} q - 6 p q^{2} - 7 q^{3}

Solution steps

(2 p + q)^{3} - (p + 2 q)^{3}

Expand

(2 p + q)^{3} : 8 p^{3} + 12 p^{2} q + 6 p q^{2} + q^{3}

= 8 p^{3} + 12 p^{2} q + 6 p q^{2} + q^{3} - (p + 2 q)^{3}

Expand

- (p + 2 q)^{3} : - p^{3} - 6 p^{2} q - 12 p q^{2} - 8 q^{3}

= 8 p^{3} + 12 p^{2} q + 6 p q^{2} + q^{3} - p^{3} - 6 p^{2} q - 12 p q^{2} - 8 q^{3}

Group like terms

= 8 p^{3} - p^{3} + 12 p^{2} q - 6 p^{2} q + 6 p q^{2} - 12 p q^{2} + q^{3} - 8 q^{3}

Add similar elements:

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

= 7 p^{3} + 12 p^{2} q - 6 p^{2} q + 6 p q^{2} - 12 p q^{2} + q^{3} - 8 q^{3}

Add similar elements:

12 p^{2} q - 6 p^{2} q = 6 p^{2} q

= 7 p^{3} + 6 p^{2} q + 6 p q^{2} - 12 p q^{2} + q^{3} - 8 q^{3}

Add similar elements:

6 p q^{2} - 12 p q^{2} = - 6 p q^{2}

= 7 p^{3} + 6 p^{2} q - 6 p q^{2} + q^{3} - 8 q^{3}

Add similar elements:

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

= 7 p^{3} + 6 p^{2} q - 6 p q^{2} - 7 q^{3}

\frac{6 y ^{4} - 3 y ^{3}}{3 y ^{3}}

(3 x - 2) (2 x - 3) - x (6 x + 13)

(7 x + 3 y)^{3}

(u^{5})^{- 2}

(a^{- 2})^{- 1} 0

What is (2p+q)^3-(p+2q)^3 ?
The solution to (2p+q)^3-(p+2q)^3 is 7p^3+6p^2q-6pq^2-7q^3