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

The solution to expand (3x^2+2x+3y^3)^2 is 9y^6+9x^4+12x^3+9x^2y^3+4x^2+12xy^3+9y^3x^2

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

expand

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

9 y^{6} + 9 x^{4} + 12 x^{3} + 9 x^{2} y^{3} + 4 x^{2} + 12 x y^{3} + 9 y^{3} x^{2}

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Distribute parentheses

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

Simplify

3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 x + 3 x^{2} \cdot 3 y^{3} + 2 x \cdot 3 x^{2} + 2 x \cdot 2 x + 2 x \cdot 3 y^{3} + 3 y^{3} \cdot 3 x^{2} + 3 y^{3} \cdot 2 x + 3 y^{3} \cdot 3 y^{3} : 9 y^{6} + 9 x^{4} + 12 x^{3} + 9 x^{2} y^{3} + 4 x^{2} + 12 x y^{3} + 9 y^{3} x^{2}

= 9 y^{6} + 9 x^{4} + 12 x^{3} + 9 x^{2} y^{3} + 4 x^{2} + 12 x y^{3} + 9 y^{3} x^{2}

lo g_{2} (128)

(x^{6} - 1)^{2}

2 x^{2} + 6 x - 5 - 7 x^{2} + 3 x + 4

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

\frac{3}{4} x^{4}

What is expand (3x^2+2x+3y^3)^2 ?
The solution to expand (3x^2+2x+3y^3)^2 is 9y^6+9x^4+12x^3+9x^2y^3+4x^2+12xy^3+9y^3x^2