What is factor (a+b)^3-(a-b)^3-2b ?

The solution to factor (a+b)^3-(a-b)^3-2b is 2b(b^2+3a^2-1)

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factor (a+b)^3-(a-b)^3-2b

factor

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

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

Solution steps

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

(a + b)^{3} : a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

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

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

= a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - a^{3} + 3 a^{2} b - 3 a b^{2} + b^{3} - 2 b

Simplify

a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - a^{3} + 3 a^{2} b - 3 a b^{2} + b^{3} - 2 b : 2 b^{3} + 6 a^{2} b - 2 b

= 2 b^{3} + 6 a^{2} b - 2 b

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

b^{3} = b b^{2}

= 2 b b^{2} + 6 a^{2} b - 2 b

Rewrite

6

3 \cdot 2

= 2 b b^{2} + 3 \cdot 2 a^{2} b - 2 b

Factor out common term

2 b

= 2 b (b^{2} + 3 a^{2} - 1)

a^{3} b^{3} + 8 c^{3}

a d - b c - b d + a c

+ (- 2)

am + bm + a^{2} + ab

a x + a + b x + b

What is factor (a+b)^3-(a-b)^3-2b ?
The solution to factor (a+b)^3-(a-b)^3-2b is 2b(b^2+3a^2-1)