What is factor s^6t^6-u^3v^{12} ?

The solution to factor s^6t^6-u^3v^{12} is (s^2t^2-uv^4)(s^4t^4+s^2t^2uv^4+u^2v^8)

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factor s^6t^6-u^3v^{12}

factor

s^{6} t^{6} - u^{3} v^{12}

(s^{2} t^{2} - u v^{4}) (s^{4} t^{4} + s^{2} t^{2} u v^{4} + u^{2} v^{8})

Solution steps

s^{6} t^{6} - u^{3} v^{12}

Rewrite

s^{6} t^{6}

(s t)^{6}

Rewrite

u^{3} v^{12}

(u v^{4})^{3}

= (s t)^{6} - (u v^{4})^{3}

Apply exponent rule:

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

(s t)^{6} = ((s t)^{2})^{3}

= ((s t)^{2})^{3} - (u v^{4})^{3}

Apply Difference of Cubes Formula:

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

((s t)^{2})^{3} - (u v^{4})^{3} = ((s t)^{2} - u v^{4}) ((s t)^{4} + (s t)^{2} u v^{4} + (u v^{4})^{2})

= ((s t)^{2} - u v^{4}) ((s t)^{4} + (s t)^{2} u v^{4} + (u v^{4})^{2})

Simplify

((s t)^{2} - u v^{4}) ((s t)^{4} + (s t)^{2} u v^{4} + (u v^{4})^{2}) : (s^{2} t^{2} - u v^{4}) (s^{4} t^{4} + s^{2} t^{2} u v^{4} + u^{2} v^{8})

= (s^{2} t^{2} - u v^{4}) (s^{4} t^{4} + s^{2} t^{2} u v^{4} + u^{2} v^{8})

[(5 a + b) - 4]^{2}

x^{2 - 25}

(e^{2 x})^{2}

[(x + y) - 3]^{2}

(tan (x^{'}))^{^{'}}

What is factor s^6t^6-u^3v^{12} ?
The solution to factor s^6t^6-u^3v^{12} is (s^2t^2-uv^4)(s^4t^4+s^2t^2uv^4+u^2v^8)