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

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

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

p^{3} - p^{3} = 0

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

Add similar elements:

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

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

Add similar elements:

3 p q^{2} - 3 p q^{2} = 0

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

Add similar elements:

q^{3} + q^{3} = 2 q^{3}

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

x^{3^{3}}

lo g_{3} (\frac{1}{81}) + lo g_{\frac{1}{3}} (\frac{1}{81})

\frac{3 b ^{- 9}}{( 3 b ^{- 4} c ^{- 3} ) ^{- 3}}

(\frac{1}{2} a^{2} + \frac{3}{6} b) (\frac{1}{2} a^{2} - \frac{3}{6} b)

\frac{15}{39}