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

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

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expand (2a-3b)^5

expand

(2 a - 3 b)^{5}

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

Solution steps

(2 a - 3 b)^{5}

Apply binomial theorem:

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

a = 2 a, b = - 3 b

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

32 n^{2} - 50

lo g_{2}^{2} (4 n^{2})

\frac{75}{125}

(3 + 33 i)^{6}

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