What is expand (3x^4-5x^3y)^3 ?

The solution to expand (3x^4-5x^3y)^3 is 27x^{12}-135x^{11}y+225x^{10}y^2-125x^9y^3

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expand (3x^4-5x^3y)^3

expand

(3 x^{4} - 5 x^{3} y)^{3}

27 x^{12} - 135 x^{11} y + 225 x^{10} y^{2} - 125 x^{9} y^{3}

Solution steps

(3 x^{4} - 5 x^{3} y)^{3}

Apply Perfect Cube Formula:

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

(3 x^{4} - 5 x^{3} y)^{3} = (3 x^{4})^{3} - 3 (3 x^{4})^{2} \cdot 5 x^{3} y + 3 \cdot 3 x^{4} (5 x^{3} y)^{2} - (5 x^{3} y)^{3}

= (3 x^{4})^{3} - 3 (3 x^{4})^{2} \cdot 5 x^{3} y + 3 \cdot 3 x^{4} (5 x^{3} y)^{2} - (5 x^{3} y)^{3}

Simplify

(3 x^{4})^{3} - 3 (3 x^{4})^{2} \cdot 5 x^{3} y + 3 \cdot 3 x^{4} (5 x^{3} y)^{2} - (5 x^{3} y)^{3} : 27 x^{12} - 135 x^{11} y + 225 x^{10} y^{2} - 125 x^{9} y^{3}

= 27 x^{12} - 135 x^{11} y + 225 x^{10} y^{2} - 125 x^{9} y^{3}

\frac{63}{5}

- 6 y + 6 y

\frac{5 p ^{7}}{25 p ^{4}}

\frac{6 ^{17}}{6 ^{24}}

12 \frac{3}{5}

What is expand (3x^4-5x^3y)^3 ?
The solution to expand (3x^4-5x^3y)^3 is 27x^{12}-135x^{11}y+225x^{10}y^2-125x^9y^3