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

The solution to expand (3x^2+7y)^3 is 27x^6+189x^4y+441x^2y^2+343y^3

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

expand

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

27 x^{6} + 189 x^{4} y + 441 x^{2} y^{2} + 343 y^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 x^{2})^{3} + 3 (3 x^{2})^{2} \cdot 7 y + 3 \cdot 3 x^{2} (7 y)^{2} + (7 y)^{3} : 27 x^{6} + 189 x^{4} y + 441 x^{2} y^{2} + 343 y^{3}

= 27 x^{6} + 189 x^{4} y + 441 x^{2} y^{2} + 343 y^{3}

\frac{( 1 + i ) ^{11}}{32 ( 1 - i )}

(x + 6)^{2} - x (x + 12) - 7

x^{3} - 6 x^{2} + 10 x - 4

\frac{2 x}{x + 2} + \frac{x + 2}{x - 2}

6 a (b + 2 c)

What is expand (3x^2+7y)^3 ?
The solution to expand (3x^2+7y)^3 is 27x^6+189x^4y+441x^2y^2+343y^3