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

32 + 18 - 8

m^{4} + m^{2} n^{2} + n^{4}

lo g_{5} (100) - lo g_{5} (4)

(3 x - 4 y)^{3}

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

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