What is factor 64x^6-125y^3z^9 ?

The solution to factor 64x^6-125y^3z^9 is (4x^2-5yz^3)(16x^4+20x^2yz^3+25y^2z^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

factor 64x^6-125y^3z^9

factor

64 x^{6} - 125 y^{3} z^{9}

(4 x^{2} - 5 y z^{3}) (16 x^{4} + 20 x^{2} y z^{3} + 25 y^{2} z^{6})

Solution steps

64 x^{6} - 125 y^{3} z^{9}

Rewrite

64 x^{6}

(2 x)^{6}

Rewrite

125 y^{3} z^{9}

(5 y z^{3})^{3}

= (2 x)^{6} - (5 y z^{3})^{3}

Apply exponent rule:

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

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

= ((2 x)^{2})^{3} - (5 y z^{3})^{3}

Apply Difference of Cubes Formula:

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

((2 x)^{2})^{3} - (5 y z^{3})^{3} = ((2 x)^{2} - 5 y z^{3}) ((2 x)^{4} + (2 x)^{2} 5 y z^{3} + (5 y z^{3})^{2})

= ((2 x)^{2} - 5 y z^{3}) ((2 x)^{4} + (2 x)^{2} 5 y z^{3} + (5 y z^{3})^{2})

Simplify

((2 x)^{2} - 5 y z^{3}) ((2 x)^{4} + (2 x)^{2} \cdot 5 y z^{3} + (5 y z^{3})^{2}) : (4 x^{2} - 5 y z^{3}) (16 x^{4} + 20 x^{2} y z^{3} + 25 y^{2} z^{6})

= (4 x^{2} - 5 y z^{3}) (16 x^{4} + 20 x^{2} y z^{3} + 25 y^{2} z^{6})

f a c t or e (- x^{2})

f a c t or 3 a x - 3 a y - 5 b x + 5 b y

f a c t or m^{11} - 7 m^{5}

f a c t or 4 a + 4 b + v a + v b

f a c t or x^{4} + 4 x^{4}

What is factor 64x^6-125y^3z^9 ?
The solution to factor 64x^6-125y^3z^9 is (4x^2-5yz^3)(16x^4+20x^2yz^3+25y^2z^6)