What is factor 27m^3-(3m+2n)^3 ?

The solution to factor 27m^3-(3m+2n)^3 is -2n(27m^2+18mn+4n^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor 27m^3-(3m+2n)^3

factor

27 m^{3} - (3 m + 2 n)^{3}

- 2 n (27 m^{2} + 18 mn + 4 n^{2})

Solution steps

27 m^{3} - (3 m + 2 n)^{3}

Rewrite

27 m^{3} - (3 m + 2 n)^{3}

(3 m)^{3} - (3 m + 2 n)^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= - 2 n ((3 m + 2 n)^{2} + 3 m (3 m + 2 n) + 9 m^{2})

Expand

(3 m + 2 n)^{2} + 3 m (3 m + 2 n) + 9 m^{2} : 27 m^{2} + 18 mn + 4 n^{2}

= - 2 n (27 m^{2} + 18 mn + 4 n^{2})

3 x

9 π x^{2} + 12 π x + 4 π

a + (b - c)

(m + n)^{2} - 6 (m + n) + 9

A B + A B^{^{'}}

What is factor 27m^3-(3m+2n)^3 ?
The solution to factor 27m^3-(3m+2n)^3 is -2n(27m^2+18mn+4n^2)