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

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

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

factor

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

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

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

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

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

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What is factor (p+q)^3-(p-q)^3 ?
The solution to factor (p+q)^3-(p-q)^3 is 2q(3p^2+q^2)