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

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

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expand (3x+2)^5

expand

(3 x + 2)^{5}

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

Solution steps

(3 x + 2)^{5}

Apply binomial theorem:

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

a = 3 x, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{7 - 10 i}{- 6 - 6 i}

\frac{lo g _{10} ( 32 )}{lo g _{10} ( 2 )}

\frac{cos ( t )}{t}

2 ln (e)

(3 x - 8)^{2}

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