How do you multiply ${(x^{\frac{3}{2}} + \frac{2}{\sqrt{3}})}^{2}$ $(x^(3/2) + 2/sqrt3)^2$ ?

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How do you multiply ${(x^{\frac{3}{2}} + \frac{2}{\sqrt{3}})}^{2}$ $(x^(3/2) + 2/sqrt3)^2$ ?

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Answer 1 · 2017-06-09T19:12:07

See a solution process below:

Explanation:

This is a special form of quadratic:

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

Substituting $x^{\frac{3}{2}}$ $x^(3/2)$ for $a$ $a$ and $\frac{2}{\sqrt{3}}$ $2/sqrt(3)$ for $b$ $b$ gives:

${(x^{\frac{3}{2}} + b)}^{2} = {(x^{\frac{3}{2}})}^{2} + (2 \cdot x^{\frac{3}{2}} \cdot \frac{2}{\sqrt{3}}) + {(\frac{2}{\sqrt{3}})}^{2} =$ $(x^(3/2) + b)^2 = (x^(3/2))^2 + (2 * x^(3/2) * 2/sqrt(3)) + (2/sqrt(3))^2 =$

$x^{3} + \frac{4 x^{\frac{3}{2}}}{\sqrt{3}} + \frac{4}{3}$ $x^3 + (4x^(3/2))/sqrt(3) + 4/3$

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How do you multiply ${(x^{\frac{3}{2}} + \frac{2}{\sqrt{3}})}^{2}$ $(x^(3/2) + 2/sqrt3)^2$ ?

1 Answer

Explanation:

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How do you multiply ${(x^{\frac{3}{2}} + \frac{2}{\sqrt{3}})}^{2}$ $(x^(3/2) + 2/sqrt3)^2$ ?