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

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

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

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

1.2 \cdot 1 0^{2}

2 (3 b)

55

56 \cdot 23

(2 x^{2} + 7 x + 10) - (x^{2} + 2 x - 9)

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