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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply rule:

a \cdot 1 = a

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

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

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