What is expand (e^{y/4}+6)^2 ?

The solution to expand (e^{y/4}+6)^2 is e^{y/2}+12e^{y/4}+36

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expand (e^{y/4}+6)^2

expand

(e^{\frac{y}{4}} + 6)^{2}

e^{\frac{y}{2}} + 12 e^{\frac{y}{4}} + 36

Solution steps

(e^{\frac{y}{4}} + 6)^{2}

Apply Perfect Square Formula:

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

a = e^{\frac{y}{4}}, b = 6

= (e^{\frac{y}{4}})^{2} + 2 e^{\frac{y}{4}} \cdot 6 + 6^{2}

Simplify

(e^{\frac{y}{4}})^{2} + 2 e^{\frac{y}{4}} \cdot 6 + 6^{2} : e^{\frac{y}{2}} + 12 e^{\frac{y}{4}} + 36

= e^{\frac{y}{2}} + 12 e^{\frac{y}{4}} + 36

\frac{12 s + 57}{( s + 2 ) ( s + 4 )}

\frac{( 3 x + 1 ) ( 3 x - 1 )}{5 x ^{2}}

\frac{5}{( s + 3 ) ( s ^{2} + 25 )}

(\forall y) (\exists x) (x = y + 1)

\frac{x ^{2} ( x + 2 z )}{z \cdot y}

What is expand (e^{y/4}+6)^2 ?
The solution to expand (e^{y/4}+6)^2 is e^{y/2}+12e^{y/4}+36