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

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

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expand (2x+3)^5

expand

(2 x + 3)^{5}

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

Solution steps

(2 x + 3)^{5}

Apply binomial theorem:

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

a = 2 x, b = 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

f (x) = \frac{x ^{3} + 2 x ^{2} - 9 x - 18}{x ^{3} - x ^{2} - 6 x}

\frac{12}{32}

\frac{4}{5} \div \frac{3}{8}

\frac{cos ^{2} ( x ) + sin ^{2} ( x )}{cos ^{2} ( x )}

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