What is factor 1000+(b-8)^3 ?

The solution to factor 1000+(b-8)^3 is (b+2)(b^2-26b+244)

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factor 1000+(b-8)^3

factor

1000 + (b - 8)^{3}

(b + 2) (b^{2} - 26 b + 244)

Solution steps

1000 + (b - 8)^{3}

Rewrite

1000

1 0^{3}

= (b - 8)^{3} + 1 0^{3}

Apply Sum of Cubes Formula:

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

(b - 8)^{3} + 1 0^{3} = ((b - 8) + 10) ((b - 8)^{2} - 10 (b - 8) + 1 0^{2})

= ((b - 8) + 10) ((b - 8)^{2} - 10 (b - 8) + 1 0^{2})

Refine

= (b + 2) ((b - 8)^{2} - 10 (b - 8) + 100)

Expand

(b - 8)^{2} - 10 (b - 8) + 100 : b^{2} - 26 b + 244

= (b + 2) (b^{2} - 26 b + 244)

0.0551100000000 \dots (4.2)^{2} - 0.5357200000000 \dots (4.2) + 1.4468100000000 \dots

2 x^{3} - 2 x^{2} - 84 x

x^{2} + 6 x + 10 > 0

- 1 - 6 x - 6 > - 11 - 7 x

2^{2} + 2^{2} = c^{2}

What is factor 1000+(b-8)^3 ?
The solution to factor 1000+(b-8)^3 is (b+2)(b^2-26b+244)