What is expand (9x^{3/2}-3x^{5/2})^2 ?

The solution to expand (9x^{3/2}-3x^{5/2})^2 is 81x^3-54x^4+9x^5

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expand (9x^{3/2}-3x^{5/2})^2

expand

(9 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}})^{2}

81 x^{3} - 54 x^{4} + 9 x^{5}

Solution steps

(9 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(9 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}})^{2} = (9 x^{\frac{3}{2}})^{2} - 2 \cdot 9 x^{\frac{3}{2}} \cdot 3 x^{\frac{5}{2}} + (3 x^{\frac{5}{2}})^{2}

= (9 x^{\frac{3}{2}})^{2} - 2 \cdot 9 x^{\frac{3}{2}} \cdot 3 x^{\frac{5}{2}} + (3 x^{\frac{5}{2}})^{2}

(9 x^{\frac{3}{2}})^{2} = 81 x^{3}

2 \cdot 9 x^{\frac{3}{2}} \cdot 3 x^{\frac{5}{2}} = 54 x^{4}

(3 x^{\frac{5}{2}})^{2} = 9 x^{5}

= 81 x^{3} - 54 x^{4} + 9 x^{5}

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What is expand (9x^{3/2}-3x^{5/2})^2 ?
The solution to expand (9x^{3/2}-3x^{5/2})^2 is 81x^3-54x^4+9x^5