What is expand (3a+1/3)^3 ?

The solution to expand (3a+1/3)^3 is (729a^3+243a^2+27a+1)/(27)

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expand (3a+1/3)^3

expand

(3 a + \frac{1}{3})^{3}

\frac{729 a ^{3} + 243 a ^{2} + 27 a + 1}{27}

Solution steps

(3 a + \frac{1}{3})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(3 a)^{3} + 3 (3 a)^{2} \frac{1}{3} + 3 \cdot 3 a (\frac{1}{3})^{2} + (\frac{1}{3})^{3} : \frac{729 a ^{3} + 243 a ^{2} + 27 a + 1}{27}

= \frac{729 a ^{3} + 243 a ^{2} + 27 a + 1}{27}

co d (\frac{π}{2} - x)

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

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

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

(cos (π t)) (- π sin (π t)) + (4 e^{t} + 5) (e^{t})

What is expand (3a+1/3)^3 ?
The solution to expand (3a+1/3)^3 is (729a^3+243a^2+27a+1)/(27)