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

The solution to (p+2q)^3-(p-2q)^3 is 12p^2q+16q^3

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

simplify

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

12 p^{2} q + 16 q^{3}

Solution steps

(p + 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}

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

12 p q^{2} - 12 p q^{2} = 0

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

Add similar elements:

8 q^{3} + 8 q^{3} = 16 q^{3}

= 12 p^{2} q + 16 q^{3}

(a - 96)^{3}

2 x^{3} - 4 x^{2} + 2 k - 10

16 a^{8} \cdot b^{- 2}

2 x + 12 x^{16}

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