What is factor x^3y^6z^{12}-t^{12} ?

The solution to factor x^3y^6z^{12}-t^{12} is (xy^2z^4-t^4)(x^2y^4z^8+xy^2z^4t^4+t^8)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor x^3y^6z^{12}-t^{12}

factor

x^{3} y^{6} z^{12} - t^{12}

(x y^{2} z^{4} - t^{4}) (x^{2} y^{4} z^{8} + x y^{2} z^{4} t^{4} + t^{8})

Solution steps

x^{3} y^{6} z^{12} - t^{12}

Rewrite

x^{3} y^{6} z^{12}

(x y^{2} z^{4})^{3}

= (x y^{2} z^{4})^{3} - t^{12}

Apply exponent rule:

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

t^{12} = (t^{4})^{3}

= (x y^{2} z^{4})^{3} - (t^{4})^{3}

Apply Difference of Cubes Formula:

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

(x y^{2} z^{4})^{3} - (t^{4})^{3} = (x y^{2} z^{4} - t^{4}) ((x y^{2} z^{4})^{2} + x y^{2} z^{4} t^{4} + t^{8})

= (x y^{2} z^{4} - t^{4}) ((x y^{2} z^{4})^{2} + t^{4} x y^{2} z^{4} + t^{8})

Simplify

(x y^{2} z^{4} - t^{4}) ((x y^{2} z^{4})^{2} + x y^{2} z^{4} t^{4} + t^{8}) : (x y^{2} z^{4} - t^{4}) (x^{2} y^{4} z^{8} + x y^{2} z^{4} t^{4} + t^{8})

= (x y^{2} z^{4} - t^{4}) (x^{2} y^{4} z^{8} + x y^{2} z^{4} t^{4} + t^{8})

- 5 y + (- 8 x)

\frac{2 x}{x ^{2} + 4 x}

(x - 3)^{2} - 5

[sin (2 x)]^{2}

- c^{8} e^{8} n^{4} u + 22 c^{5} u^{2}

What is factor x^3y^6z^{12}-t^{12} ?
The solution to factor x^3y^6z^{12}-t^{12} is (xy^2z^4-t^4)(x^2y^4z^8+xy^2z^4t^4+t^8)