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

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

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expand (3x+2y)^5

expand

(3 x + 2 y)^{5}

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

Solution steps

(3 x + 2 y)^{5}

Apply binomial theorem:

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

a = 3 x, b = 2 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(- 4 x) (5 x)

k^{- \frac{1}{3}}

e^{4 πi}

\frac{3 x}{x - 7} + \frac{5}{7 - x}

(3 - 3 i)^{2}

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