What is expand (3a^2b^4+2a^3c^4)^3 ?

The solution to expand (3a^2b^4+2a^3c^4)^3 is 27a^6b^{12}+54a^7b^8c^4+36a^8b^4c^8+8a^9c^{12}

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expand (3a^2b^4+2a^3c^4)^3

expand

(3 a^{2} b^{4} + 2 a^{3} c^{4})^{3}

27 a^{6} b^{12} + 54 a^{7} b^{8} c^{4} + 36 a^{8} b^{4} c^{8} + 8 a^{9} c^{12}

Solution steps

(3 a^{2} b^{4} + 2 a^{3} c^{4})^{3}

Apply Perfect Cube Formula:

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

(3 a^{2} b^{4} + 2 a^{3} c^{4})^{3} = (3 a^{2} b^{4})^{3} + 3 (3 a^{2} b^{4})^{2} \cdot 2 a^{3} c^{4} + 3 \cdot 3 a^{2} b^{4} (2 a^{3} c^{4})^{2} + (2 a^{3} c^{4})^{3}

= (3 a^{2} b^{4})^{3} + 3 (3 a^{2} b^{4})^{2} \cdot 2 a^{3} c^{4} + 3 \cdot 3 a^{2} b^{4} (2 a^{3} c^{4})^{2} + (2 a^{3} c^{4})^{3}

Simplify

(3 a^{2} b^{4})^{3} + 3 (3 a^{2} b^{4})^{2} \cdot 2 a^{3} c^{4} + 3 \cdot 3 a^{2} b^{4} (2 a^{3} c^{4})^{2} + (2 a^{3} c^{4})^{3} : 27 a^{6} b^{12} + 54 a^{7} b^{8} c^{4} + 36 a^{8} b^{4} c^{8} + 8 a^{9} c^{12}

= 27 a^{6} b^{12} + 54 a^{7} b^{8} c^{4} + 36 a^{8} b^{4} c^{8} + 8 a^{9} c^{12}

\frac{5 + 1}{2}

\frac{1}{10} - \frac{9}{10}

(5^{5})^{4}

12 - 3

\frac{2}{11} + \frac{1}{2}

What is expand (3a^2b^4+2a^3c^4)^3 ?
The solution to expand (3a^2b^4+2a^3c^4)^3 is 27a^6b^{12}+54a^7b^8c^4+36a^8b^4c^8+8a^9c^{12}