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

The solution to expand (2a-3b)^3 is 8a^3-36a^2b+54ab^2-27b^3

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expand (2a-3b)^3

expand

(2 a - 3 b)^{3}

8 a^{3} - 36 a^{2} b + 54 a b^{2} - 27 b^{3}

Solution steps

(2 a - 3 b)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 a)^{3} - 3 (2 a)^{2} \cdot 3 b + 3 \cdot 2 a (3 b)^{2} - (3 b)^{3} : 8 a^{3} - 36 a^{2} b + 54 a b^{2} - 27 b^{3}

= 8 a^{3} - 36 a^{2} b + 54 a b^{2} - 27 b^{3}

\frac{- 3}{6}

(3 x^{2} - 1)^{2}

(2 x^{2} + 5) + (x^{3} - 5 x^{2} - 2 x + 3)

\frac{4}{64}

- 3 + \frac{3}{2}

What is expand (2a-3b)^3 ?
The solution to expand (2a-3b)^3 is 8a^3-36a^2b+54ab^2-27b^3