What is factor a^6b^6-8c^3 ?

The solution to factor a^6b^6-8c^3 is (a^2b^2-2c)(a^4b^4+2a^2b^2c+4c^2)

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factor a^6b^6-8c^3

factor

a^{6} b^{6} - 8 c^{3}

(a^{2} b^{2} - 2 c) (a^{4} b^{4} + 2 a^{2} b^{2} c + 4 c^{2})

Solution steps

a^{6} b^{6} - 8 c^{3}

Rewrite

a^{6} b^{6}

(ab)^{6}

Rewrite

8 c^{3}

(2 c)^{3}

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

Apply exponent rule:

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

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

= ((ab)^{2})^{3} - (2 c)^{3}

Apply Difference of Cubes Formula:

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

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

= ((ab)^{2} - 2 c) ((ab)^{4} + (ab)^{2} 2 c + (2 c)^{2})

Simplify

((ab)^{2} - 2 c) ((ab)^{4} + (ab)^{2} \cdot 2 c + (2 c)^{2}) : (a^{2} b^{2} - 2 c) (a^{4} b^{4} + 2 a^{2} b^{2} c + 4 c^{2})

= (a^{2} b^{2} - 2 c) (a^{4} b^{4} + 2 a^{2} b^{2} c + 4 c^{2})

B a (N O^{3}) 2

2 x + 4 y + x z + 2 yz

(tan (t))^{2}

sin (x^{3} - 1)

π \cdot (4)

What is factor a^6b^6-8c^3 ?
The solution to factor a^6b^6-8c^3 is (a^2b^2-2c)(a^4b^4+2a^2b^2c+4c^2)