What is factor 27m^6+343n^9 ?

The solution to factor 27m^6+343n^9 is (3m^2+7n^3)(9m^4-21m^2n^3+49n^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor 27m^6+343n^9

factor

27 m^{6} + 343 n^{9}

(3 m^{2} + 7 n^{3}) (9 m^{4} - 21 m^{2} n^{3} + 49 n^{6})

Solution steps

27 m^{6} + 343 n^{9}

Apply exponent rules

= (3 m^{2})^{3} + (7 n^{3})^{3}

Apply Sum of Cubes Formula:

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

(3 m^{2})^{3} + (7 n^{3})^{3} = (3 m^{2} + 7 n^{3}) ((3 m^{2})^{2} - 3 m^{2} \cdot 7 n^{3} + (7 n^{3})^{2})

= (3 m^{2} + 7 n^{3}) ((3 m^{2})^{2} - 3 m^{2} \cdot 7 n^{3} + (7 n^{3})^{2})

Simplify

(3 m^{2})^{2} - 3 m^{2} \cdot 7 n^{3} + (7 n^{3})^{2} : 9 m^{4} - 21 m^{2} n^{3} + 49 n^{6}

= (3 m^{2} + 7 n^{3}) (9 m^{4} - 21 m^{2} n^{3} + 49 n^{6})

9 x < - 12 + 3 x

2 5^{- \frac{1}{3}}

x^{2} - 5 x + 12 = 2 x + 6

4 x + 7 = 9 x - 3

20 x^{2} - 9 x - 20 > 0

What is factor 27m^6+343n^9 ?
The solution to factor 27m^6+343n^9 is (3m^2+7n^3)(9m^4-21m^2n^3+49n^6)