What is expand (6x^2-5y)^3 ?

The solution to expand (6x^2-5y)^3 is 216x^6-540x^4y+450x^2y^2-125y^3

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expand (6x^2-5y)^3

expand

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

216 x^{6} - 540 x^{4} y + 450 x^{2} y^{2} - 125 y^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

(6 x^{2} - 5 y)^{3} = (6 x^{2})^{3} - 3 (6 x^{2})^{2} \cdot 5 y + 3 \cdot 6 x^{2} (5 y)^{2} - (5 y)^{3}

= (6 x^{2})^{3} - 3 (6 x^{2})^{2} \cdot 5 y + 3 \cdot 6 x^{2} (5 y)^{2} - (5 y)^{3}

Simplify

(6 x^{2})^{3} - 3 (6 x^{2})^{2} \cdot 5 y + 3 \cdot 6 x^{2} (5 y)^{2} - (5 y)^{3} : 216 x^{6} - 540 x^{4} y + 450 x^{2} y^{2} - 125 y^{3}

= 216 x^{6} - 540 x^{4} y + 450 x^{2} y^{2} - 125 y^{3}

\frac{5 - 80 x ^{2}}{10}

\frac{5}{7} \cdot \frac{3}{4}

- 3 \frac{1}{4}

5 x^{2} + 6 x - 3 + 4 x^{2} - 8 x + 2

\frac{79}{8}

What is expand (6x^2-5y)^3 ?
The solution to expand (6x^2-5y)^3 is 216x^6-540x^4y+450x^2y^2-125y^3