What is expand (5x^2+7y^3)^3 ?

The solution to expand (5x^2+7y^3)^3 is 125x^6+525x^4y^3+735x^2y^6+343y^9

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expand (5x^2+7y^3)^3

expand

(5 x^{2} + 7 y^{3})^{3}

125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

Solution steps

(5 x^{2} + 7 y^{3})^{3}

Apply Perfect Cube Formula:

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

(5 x^{2} + 7 y^{3})^{3} = (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3}

= (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3}

Simplify

(5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3} : 125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

= 125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

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

\frac{x ^{2} \cdot 1}{3 ( x ^{5} )}

2 cos^{2} (5 x) - 1

(a - b)^{3} + (b - c)^{3} + (c - a)^{3}

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

What is expand (5x^2+7y^3)^3 ?
The solution to expand (5x^2+7y^3)^3 is 125x^6+525x^4y^3+735x^2y^6+343y^9