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

The solution to factor (a+b)^3-1000c^3 is (a+b-10c)((a+b)^2+10c(a+b)+100c^2)

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factor (a+b)^3-1000c^3

factor

(a + b)^{3} - 1000 c^{3}

(a + b - 10 c) ((a + b)^{2} + 10 c (a + b) + 100 c^{2})

Solution steps

(a + b)^{3} - 1000 c^{3}

Rewrite

(a + b)^{3} - 1000 c^{3}

(a + b)^{3} - (10 c)^{3}

= (a + b)^{3} - (10 c)^{3}

Apply Difference of Cubes Formula:

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

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

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

Refine

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

x^{6} + 6 x^{4} + 12 x^{2} + 8

e^{2} - e

\cdot (- 3)

sin^{3} (x) - cos^{3} (x)

[5.9]

What is factor (a+b)^3-1000c^3 ?
The solution to factor (a+b)^3-1000c^3 is (a+b-10c)((a+b)^2+10c(a+b)+100c^2)