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}

6 x - 3 x + 2 x^{2} + 3 x + x^{2}

\frac{9 x ^{8} y ^{7}}{27 x y ^{3}}

\frac{\frac{x}{9}}{9}

\frac{3 + 5 i}{5 i}

\frac{9}{7} - \frac{7}{10}

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