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

The solution to expand (a^2-2b)^3 is a^6-6a^4b+12a^2b^2-8b^3

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expand (a^2-2b)^3

expand

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

a^{6} - 6 a^{4} b + 12 a^{2} b^{2} - 8 b^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(a^{2})^{3} - 3 (a^{2})^{2} \cdot 2 b + 3 a^{2} (2 b)^{2} - (2 b)^{3} : a^{6} - 6 a^{4} b + 12 a^{2} b^{2} - 8 b^{3}

= a^{6} - 6 a^{4} b + 12 a^{2} b^{2} - 8 b^{3}

\frac{3 ( 1 - 2 )}{3}

(m - n) (m + n)

\frac{( 4.13566 \cdot 1 0 ^{- 15} ) \cdot ( 3 \cdot 1 0 ^{8} )}{3 \cdot ( 10.3 )}

(2 x - 2)^{2}

3 x^{2}

What is expand (a^2-2b)^3 ?
The solution to expand (a^2-2b)^3 is a^6-6a^4b+12a^2b^2-8b^3