What is expand (3a^2b-5a^3b^2)^3 ?

The solution to expand (3a^2b-5a^3b^2)^3 is 27a^6b^3-135a^7b^4+225a^8b^5-125a^9b^6

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expand (3a^2b-5a^3b^2)^3

expand

(3 a^{2} b - 5 a^{3} b^{2})^{3}

27 a^{6} b^{3} - 135 a^{7} b^{4} + 225 a^{8} b^{5} - 125 a^{9} b^{6}

Solution steps

(3 a^{2} b - 5 a^{3} b^{2})^{3}

Apply Perfect Cube Formula:

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

(3 a^{2} b - 5 a^{3} b^{2})^{3} = (3 a^{2} b)^{3} - 3 (3 a^{2} b)^{2} \cdot 5 a^{3} b^{2} + 3 \cdot 3 a^{2} b (5 a^{3} b^{2})^{2} - (5 a^{3} b^{2})^{3}

= (3 a^{2} b)^{3} - 3 (3 a^{2} b)^{2} \cdot 5 a^{3} b^{2} + 3 \cdot 3 a^{2} b (5 a^{3} b^{2})^{2} - (5 a^{3} b^{2})^{3}

Simplify

(3 a^{2} b)^{3} - 3 (3 a^{2} b)^{2} \cdot 5 a^{3} b^{2} + 3 \cdot 3 a^{2} b (5 a^{3} b^{2})^{2} - (5 a^{3} b^{2})^{3} : 27 a^{6} b^{3} - 135 a^{7} b^{4} + 225 a^{8} b^{5} - 125 a^{9} b^{6}

= 27 a^{6} b^{3} - 135 a^{7} b^{4} + 225 a^{8} b^{5} - 125 a^{9} b^{6}

4 + 625 y^{8}

x^{2} + \frac{1}{9} + \frac{( 2 x )}{3}

6 x [3 + (10 + 26)]

3 x (2 - 2 x + 3)

\frac{( 3 ^{x + l} + 3 ^{x} )}{( 3 ^{x + 3} - 3 ^{x + l} )}

What is expand (3a^2b-5a^3b^2)^3 ?
The solution to expand (3a^2b-5a^3b^2)^3 is 27a^6b^3-135a^7b^4+225a^8b^5-125a^9b^6