What is expand (3+2x)^5 ?

The solution to expand (3+2x)^5 is 243+810x+1080x^2+720x^3+240x^4+32x^5

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expand (3+2x)^5

expand

(3 + 2 x)^{5}

243 + 810 x + 1080 x^{2} + 720 x^{3} + 240 x^{4} + 32 x^{5}

Solution steps

(3 + 2 x)^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 3, b = 2 x

= i = 0 \sum 5 (i 5) \cdot 3^{(5 - i)} (2 x)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (2 x)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (2 x)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (2 x)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (2 x)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (2 x)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (2 x)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (2 x)^{0} : 243

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (2 x)^{1} : 810 x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (2 x)^{2} : 1080 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (2 x)^{3} : 720 x^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (2 x)^{4} : 240 x^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (2 x)^{5} : 32 x^{5}

= 243 + 810 x + 1080 x^{2} + 720 x^{3} + 240 x^{4} + 32 x^{5}

\frac{cot ( θ )}{csc ( θ )}

(- 2^{3})^{- 2}

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

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

ln ((2 x e^{β})^{2}) + e^{(β + l n (3 x))}

What is expand (3+2x)^5 ?
The solution to expand (3+2x)^5 is 243+810x+1080x^2+720x^3+240x^4+32x^5