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

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

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expand (2+3x)^5

expand

(2 + 3 x)^{5}

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

Solution steps

(2 + 3 x)^{5}

Apply binomial theorem:

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

a = 2, b = 3 x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

x \cdot (- x^{2})

\frac{1 0 ^{3}}{1 0 ^{- 5}}

a^{2} b^{2}

\frac{200}{9}

3.5 (2 x + 4) - 4 (x - 2.5)

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