What is expand (3a+2b)^5 ?

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

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expand (3a+2b)^5

expand

(3 a + 2 b)^{5}

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

Solution steps

(3 a + 2 b)^{5}

Apply binomial theorem:

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

a = 3 a, b = 2 b

= i = 0 \sum 5 (i 5) (3 a)^{(5 - i)} (2 b)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 a)^{5} (2 b)^{0} : 243 a^{5}

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 a)^{3} (2 b)^{2} : 1080 a^{3} b^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 a)^{2} (2 b)^{3} : 720 a^{2} b^{3}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 a)^{0} (2 b)^{5} : 32 b^{5}

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

(- 5 x^{2} + 5 x) - (- 8 x^{2} - 9)

(18)^{2}

(7 a + 5 b) (7 a - 5 b)

2 (2 x + 1) + 1

(2^{- 1} + 3^{- 1})^{- 1}

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