What is expand (x^{3/2}+1)^2 ?

The solution to expand (x^{3/2}+1)^2 is x^3+2x^{3/2}+1

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expand (x^{3/2}+1)^2

expand

(x^{\frac{3}{2}} + 1)^{2}

x^{3} + 2 x^{\frac{3}{2}} + 1

Solution steps

(x^{\frac{3}{2}} + 1)^{2}

Apply Perfect Square Formula:

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

(x^{\frac{3}{2}} + 1)^{2} = (x^{\frac{3}{2}})^{2} + 2 x^{\frac{3}{2}} \cdot 1 + 1^{2}

= (x^{\frac{3}{2}})^{2} + 2 x^{\frac{3}{2}} \cdot 1 + 1^{2}

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

2 x^{\frac{3}{2}} \cdot 1 = 2 x^{\frac{3}{2}}

1^{2} = 1

= x^{3} + 2 x^{\frac{3}{2}} + 1

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What is expand (x^{3/2}+1)^2 ?
The solution to expand (x^{3/2}+1)^2 is x^3+2x^{3/2}+1