What is factor (2x+1)^3-8 ?

The solution to factor (2x+1)^3-8 is (2x-1)(4x^2+8x+7)

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factor (2x+1)^3-8

factor

(2 x + 1)^{3} - 8

(2 x - 1) (4 x^{2} + 8 x + 7)

Solution steps

(2 x + 1)^{3} - 8

Rewrite

8

2^{3}

= (2 x + 1)^{3} - 2^{3}

Apply Difference of Cubes Formula:

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

(2 x + 1)^{3} - 2^{3} = ((2 x + 1) - 2) ((2 x + 1)^{2} + 2 (2 x + 1) + 2^{2})

= ((2 x + 1) - 2) ((2 x + 1)^{2} + 2 (2 x + 1) + 2^{2})

Refine

= (2 x - 1) ((2 x + 1)^{2} + 2 (2 x + 1) + 4)

Expand

(2 x + 1)^{2} + 2 (2 x + 1) + 4 : 4 x^{2} + 8 x + 7

= (2 x - 1) (4 x^{2} + 8 x + 7)

x^{3} + 2 x - 5 x - 6

9 x^{2} + (54) x + (86)

(2 + x)^{3} - 216

2 a c^{2} + b c^{2} - 2 a c - b c - 2 a - b

v (- 1.2)

What is factor (2x+1)^3-8 ?
The solution to factor (2x+1)^3-8 is (2x-1)(4x^2+8x+7)