What is expand (5x-8y)^3 ?

The solution to expand (5x-8y)^3 is 125x^3-600x^2y+960xy^2-512y^3

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expand (5x-8y)^3

expand

(5 x - 8 y)^{3}

125 x^{3} - 600 x^{2} y + 960 x y^{2} - 512 y^{3}

Solution steps

(5 x - 8 y)^{3}

Apply Perfect Cube Formula:

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

(5 x - 8 y)^{3} = (5 x)^{3} - 3 (5 x)^{2} \cdot 8 y + 3 \cdot 5 x (8 y)^{2} - (8 y)^{3}

= (5 x)^{3} - 3 (5 x)^{2} \cdot 8 y + 3 \cdot 5 x (8 y)^{2} - (8 y)^{3}

Simplify

(5 x)^{3} - 3 (5 x)^{2} \cdot 8 y + 3 \cdot 5 x (8 y)^{2} - (8 y)^{3} : 125 x^{3} - 600 x^{2} y + 960 x y^{2} - 512 y^{3}

= 125 x^{3} - 600 x^{2} y + 960 x y^{2} - 512 y^{3}

\frac{( 4 x \cdot y ^{2} + 2 x ^{2} \cdot y ^{2} - 2 x \cdot y ^{3} )}{( 2 x ^{2} \cdot y ^{2} )}

\frac{( 8 )}{( 3 x )}

9 u^{2} v^{4} - u^{2} v^{2}

(- 1 + i) \cdot (- i^{k})

2 x^{2} + \frac{( 5 x )}{2} + \frac{1}{2}

What is expand (5x-8y)^3 ?
The solution to expand (5x-8y)^3 is 125x^3-600x^2y+960xy^2-512y^3