What is expand (3c^3d^2-2abc)^3 ?

The solution to expand (3c^3d^2-2abc)^3 is 27c^9d^6-54c^7d^4ab+36c^5d^2a^2b^2-8a^3b^3c^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3c^3d^2-2abc)^3

expand

(3 c^{3} d^{2} - 2 ab c)^{3}

27 c^{9} d^{6} - 54 c^{7} d^{4} ab + 36 c^{5} d^{2} a^{2} b^{2} - 8 a^{3} b^{3} c^{3}

Solution steps

(3 c^{3} d^{2} - 2 ab c)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(3 c^{3} d^{2} - 2 ab c)^{3} = (3 c^{3} d^{2})^{3} - 3 (3 c^{3} d^{2})^{2} \cdot 2 ab c + 3 \cdot 3 c^{3} d^{2} (2 ab c)^{2} - (2 ab c)^{3}

= (3 c^{3} d^{2})^{3} - 3 (3 c^{3} d^{2})^{2} \cdot 2 ab c + 3 \cdot 3 c^{3} d^{2} (2 ab c)^{2} - (2 ab c)^{3}

Simplify

(3 c^{3} d^{2})^{3} - 3 (3 c^{3} d^{2})^{2} \cdot 2 ab c + 3 \cdot 3 c^{3} d^{2} (2 ab c)^{2} - (2 ab c)^{3} : 27 c^{9} d^{6} - 54 c^{7} d^{4} ab + 36 c^{5} d^{2} a^{2} b^{2} - 8 a^{3} b^{3} c^{3}

= 27 c^{9} d^{6} - 54 c^{7} d^{4} ab + 36 c^{5} d^{2} a^{2} b^{2} - 8 a^{3} b^{3} c^{3}

\frac{2}{3} x^{4}

\frac{3}{5 - 2}

(8 k + k^{2} - 6) - (- 10 k + 7 - 2 k^{2})

(x - 3) (x^{2} - 9 x)

\frac{121}{10}

What is expand (3c^3d^2-2abc)^3 ?
The solution to expand (3c^3d^2-2abc)^3 is 27c^9d^6-54c^7d^4ab+36c^5d^2a^2b^2-8a^3b^3c^3