What is factor (x+1)^3+1728 ?

The solution to factor (x+1)^3+1728 is (x+13)(x^2-10x+133)

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factor (x+1)^3+1728

factor

(x + 1)^{3} + 1728

(x + 13) (x^{2} - 10 x + 133)

Solution steps

(x + 1)^{3} + 1728

Rewrite

1728

1 2^{3}

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

Apply Sum of Cubes Formula:

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

(x + 1)^{3} + 1 2^{3} = ((x + 1) + 12) ((x + 1)^{2} - 12 (x + 1) + 1 2^{2})

= ((x + 1) + 12) ((x + 1)^{2} - 12 (x + 1) + 1 2^{2})

Refine

= (x + 13) ((x + 1)^{2} - 12 (x + 1) + 144)

Expand

(x + 1)^{2} - 12 (x + 1) + 144 : x^{2} - 10 x + 133

= (x + 13) (x^{2} - 10 x + 133)

x^{7}

vx + 6 gx + v q + 6 g q

in (e^{3})

1 6^{2} - 2 5^{2}

(7 h + 1) + 7 h^{2}

What is factor (x+1)^3+1728 ?
The solution to factor (x+1)^3+1728 is (x+13)(x^2-10x+133)