What is factor a^6b^6-1000x^3 ?

The solution to factor a^6b^6-1000x^3 is (a^2b^2-10x)(a^4b^4+10a^2b^2x+100x^2)

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factor a^6b^6-1000x^3

factor

a^{6} b^{6} - 1000 x^{3}

(a^{2} b^{2} - 10 x) (a^{4} b^{4} + 10 a^{2} b^{2} x + 100 x^{2})

Solution steps

a^{6} b^{6} - 1000 x^{3}

Rewrite

a^{6} b^{6}

(ab)^{6}

Rewrite

1000 x^{3}

(10 x)^{3}

= (ab)^{6} - (10 x)^{3}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

(ab)^{6} = ((ab)^{2})^{3}

= ((ab)^{2})^{3} - (10 x)^{3}

Apply Difference of Cubes Formula:

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

((ab)^{2})^{3} - (10 x)^{3} = ((ab)^{2} - 10 x) ((ab)^{4} + 10 x (ab)^{2} + (10 x)^{2})

= ((ab)^{2} - 10 x) ((10 x)^{2} + 10 x (ab)^{2} + (ab)^{4})

Simplify

((ab)^{2} - 10 x) ((ab)^{4} + 10 x (ab)^{2} + (10 x)^{2}) : (a^{2} b^{2} - 10 x) (a^{4} b^{4} + 10 a^{2} b^{2} x + 100 x^{2})

= (a^{2} b^{2} - 10 x) (a^{4} b^{4} + 10 a^{2} b^{2} x + 100 x^{2})

(m^{2} - n^{2}) + 2 mn

arctan (x) (2 x)

in t (6 x^{2})

48 d^{2} e - 32 d

[(5 a + 1) + 2 y]^{2}

What is factor a^6b^6-1000x^3 ?
The solution to factor a^6b^6-1000x^3 is (a^2b^2-10x)(a^4b^4+10a^2b^2x+100x^2)