Question 148115
*[Tex \LARGE \left(3x^{\frac{2}{3}}+2\right)^{2}] Start with the given expression.



*[Tex \LARGE \left(3x^{\frac{2}{3}}+2\right)\left(3x^{\frac{2}{3}}+2\right)] Expand. Remember, {{{x^2=x*x}}}



*[Tex \LARGE \left(3x^{\frac{2}{3}\right)\left(3x^{\frac{2}{3}\right) + \left(3x^{\frac{2}{3}\right)\left(2\right) + \left(2\right)\left(3x^{\frac{2}{3}\right)+ \left(2\right)\left(2\right)] Foil.



*[Tex \LARGE 9x^{\frac{4}{3}} + \left(3x^{\frac{2}{3}\right)\left(2\right) + \left(2\right)\left(3x^{\frac{2}{3}\right)+ \left(2\right)\left(2\right)] Multiply *[Tex \LARGE 3x^{\frac{2}{3}] and *[Tex \LARGE 3x^{\frac{2}{3}] to get *[Tex \LARGE \left(3x^{\frac{2}{3}\right)\left(3x^{\frac{2}{3}\right)=\left(3*3\right)x^{\frac{2}{3}+\frac{2}{3}}=9x^{\frac{4}{3}}]




*[Tex \LARGE 9x^{\frac{4}{3}}+6x^{\frac{2}{3}}+6x^{\frac{2}{3}} \left(2\right)\left(2\right)] Multiply *[Tex \LARGE 3x^{\frac{2}{3}] and *[Tex \LARGE 2] to get *[Tex \LARGE 6x^{\frac{2}{3}}]. Note: this happens twice since the multiplication order does not matter.



*[Tex \LARGE 9x^{\frac{4}{3}} +6x^{\frac{2}{3}}+6x^{\frac{2}{3}}+ 4] Multiply *[Tex \LARGE 2] and *[Tex \LARGE 2] to get *[Tex \LARGE 4]. 



*[Tex \LARGE 9x^{\frac{4}{3}} +12x^{\frac{2}{3}} +4] Combine like terms.



So *[Tex \LARGE \left(3x^{\frac{2}{3}}+2\right)^{2}] FOILs and multiplies to *[Tex \LARGE 9x^{\frac{4}{3}} +12x^{\frac{2}{3}} +4]



In other words, *[Tex \LARGE \left(3x^{\frac{2}{3}}+2\right)^{2}=9x^{\frac{4}{3}} +12x^{\frac{2}{3}} +4]