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

The solution to expand (2a-2b)^5 is 32a^5-160a^4b+320a^3b^2-320a^2b^3+160ab^4-32b^5

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expand (2a-2b)^5

expand

(2 a - 2 b)^{5}

32 a^{5} - 160 a^{4} b + 320 a^{3} b^{2} - 320 a^{2} b^{3} + 160 a b^{4} - 32 b^{5}

Solution steps

(2 a - 2 b)^{5}

Apply binomial theorem:

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

a = 2 a, b = - 2 b

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 a)^{4} (- 2 b)^{1} : - 160 a^{4} b

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 a)^{3} (- 2 b)^{2} : 320 a^{3} b^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 a)^{2} (- 2 b)^{3} : - 320 a^{2} b^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 a)^{1} (- 2 b)^{4} : 160 a b^{4}

Simplify

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

= 32 a^{5} - 160 a^{4} b + 320 a^{3} b^{2} - 320 a^{2} b^{3} + 160 a b^{4} - 32 b^{5}

(- 4 - 7 i)^{2}

(2 - 3 x)^{4}

\frac{1}{5} - \frac{9}{64}

y^{2} - 13 y + 12

0.064

What is expand (2a-2b)^5 ?
The solution to expand (2a-2b)^5 is 32a^5-160a^4b+320a^3b^2-320a^2b^3+160ab^4-32b^5