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

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

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

expand

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

8 a^{6} b^{3} + 36 a^{7} b^{4} + 54 a^{8} b^{5} + 27 a^{9} b^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

= 8 a^{6} b^{3} + 36 a^{7} b^{4} + 54 a^{8} b^{5} + 27 a^{9} b^{6}

(x^{2} - 7 x + 1) - (3 x^{2} - 7 x + 4)

sin^{4} (x) - 1

25 x^{2} - 100 x \cdot y^{2} + 100 y^{4}

\frac{\frac{1}{10} v}{v}

x^{2} ln (y^{3})

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