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

The solution to factor (a+b)^3-(b-c)^3 is (a+c)(3b^2+3ab-3bc+a^2+c^2-ac)

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factor (a+b)^3-(b-c)^3

factor

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

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

Solution steps

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

Apply Difference of Cubes Formula:

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

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

= ((a + b) - (b - c)) ((b - c)^{2} + (b - c) (a + b) + (a + b)^{2})

Refine

= (a + c) ((a + b)^{2} + (b - c) (a + b) + (b - c)^{2})

Expand

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

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

2 (x + 1) - 4 (x + 1)

1 6^{4} - 81

2 x^{2} - a x^{2} - 2 y + a y

8 e^{3} f^{6} - 125 g^{3}

(cos (11 x))^{2}

What is factor (a+b)^3-(b-c)^3 ?
The solution to factor (a+b)^3-(b-c)^3 is (a+c)(3b^2+3ab-3bc+a^2+c^2-ac)