What is factor (a+b)^3-8 ?

The solution to factor (a+b)^3-8 is (a+b-2)((a+b)^2+2(a+b)+4)

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factor (a+b)^3-8

factor

(a + b)^{3} - 8

(a + b - 2) ((a + b)^{2} + 2 (a + b) + 4)

Solution steps

(a + b)^{3} - 8

Rewrite

8

2^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (a + b - 2) ((a + b)^{2} + 2 (a + b) + 4)

4 x^{3} + 48 x^{2} + 128 x

x^{2} + 12 x + 52 = 0

(\frac{1}{2} t^{2})^{2}

(8 x - 6)^{2} + (8 x - 6) (5 x - 4)

\frac{f}{2} - 22 < 48

What is factor (a+b)^3-8 ?
The solution to factor (a+b)^3-8 is (a+b-2)((a+b)^2+2(a+b)+4)