What is expand (2a-4b)^4 ?

The solution to expand (2a-4b)^4 is 16a^4-128a^3b+384a^2b^2-512ab^3+256b^4

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expand (2a-4b)^4

expand

(2 a - 4 b)^{4}

16 a^{4} - 128 a^{3} b + 384 a^{2} b^{2} - 512 a b^{3} + 256 b^{4}

Solution steps

(2 a - 4 b)^{4}

Apply binomial theorem:

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

a = 2 a, b = - 4 b

= i = 0 \sum 4 (i 4) (2 a)^{(4 - i)} (- 4 b)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 a)^{4} (- 4 b)^{0} : 16 a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 a)^{3} (- 4 b)^{1} : - 128 a^{3} b

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 a)^{2} (- 4 b)^{2} : 384 a^{2} b^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 a)^{1} (- 4 b)^{3} : - 512 a b^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 a)^{0} (- 4 b)^{4} : 256 b^{4}

= 16 a^{4} - 128 a^{3} b + 384 a^{2} b^{2} - 512 a b^{3} + 256 b^{4}

\frac{7}{3 5}

\frac{10 6}{3}

4 x - 10 x + 13 + 4 y

5 - \frac{1}{2} i

x^{2} + x^{8}

What is expand (2a-4b)^4 ?
The solution to expand (2a-4b)^4 is 16a^4-128a^3b+384a^2b^2-512ab^3+256b^4