What is expand (5p^2-4q)^3 ?

The solution to expand (5p^2-4q)^3 is 125p^6-300p^4q+240p^2q^2-64q^3

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expand (5p^2-4q)^3

expand

(5 p^{2} - 4 q)^{3}

125 p^{6} - 300 p^{4} q + 240 p^{2} q^{2} - 64 q^{3}

Solution steps

(5 p^{2} - 4 q)^{3}

Apply Perfect Cube Formula:

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

(5 p^{2} - 4 q)^{3} = (5 p^{2})^{3} - 3 (5 p^{2})^{2} \cdot 4 q + 3 \cdot 5 p^{2} (4 q)^{2} - (4 q)^{3}

= (5 p^{2})^{3} - 3 (5 p^{2})^{2} \cdot 4 q + 3 \cdot 5 p^{2} (4 q)^{2} - (4 q)^{3}

Simplify

(5 p^{2})^{3} - 3 (5 p^{2})^{2} \cdot 4 q + 3 \cdot 5 p^{2} (4 q)^{2} - (4 q)^{3} : 125 p^{6} - 300 p^{4} q + 240 p^{2} q^{2} - 64 q^{3}

= 125 p^{6} - 300 p^{4} q + 240 p^{2} q^{2} - 64 q^{3}

\frac{4}{3}

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

\frac{5}{8} - \frac{9}{32}

\frac{( \frac{1}{x} - 1 )}{x - 1}

(3 x + 6 y) (x^{2} + 4 x y - 5 y^{2})

What is expand (5p^2-4q)^3 ?
The solution to expand (5p^2-4q)^3 is 125p^6-300p^4q+240p^2q^2-64q^3