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

The solution to expand (2x^2+3y)^3 is 8x^6+36x^4y+54x^2y^2+27y^3

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

expand

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

8 x^{6} + 36 x^{4} y + 54 x^{2} y^{2} + 27 y^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 3 y + 3 \cdot 2 x^{2} (3 y)^{2} + (3 y)^{3} : 8 x^{6} + 36 x^{4} y + 54 x^{2} y^{2} + 27 y^{3}

= 8 x^{6} + 36 x^{4} y + 54 x^{2} y^{2} + 27 y^{3}

- 8 \times 3

\frac{100}{3}

\frac{( x ^{2} - 4 )}{( x - 2 )}

x^{3} \cdot 2 x

ln (0.15)

What is expand (2x^2+3y)^3 ?
The solution to expand (2x^2+3y)^3 is 8x^6+36x^4y+54x^2y^2+27y^3