What is expand (2x+4)^4 ?

The solution to expand (2x+4)^4 is 16x^4+128x^3+384x^2+512x+256

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expand (2x+4)^4

expand

(2 x + 4)^{4}

16 x^{4} + 128 x^{3} + 384 x^{2} + 512 x + 256

Solution steps

(2 x + 4)^{4}

Apply binomial theorem:

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

a = 2 x, b = 4

= i = 0 \sum 4 (i 4) (2 x)^{(4 - i)} \cdot 4^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 x)^{4} \cdot 4^{0} : 16 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 x)^{3} \cdot 4^{1} : 128 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 x)^{2} \cdot 4^{2} : 384 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 x)^{1} \cdot 4^{3} : 512 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 x)^{0} \cdot 4^{4} : 256

= 16 x^{4} + 128 x^{3} + 384 x^{2} + 512 x + 256

\frac{2}{4 - 3}

12 + (- 10)

\frac{3}{5} - \frac{1}{8}

\frac{12}{13}

\frac{( sec ^{2} ( x ) )}{tan ( x )}

What is expand (2x+4)^4 ?
The solution to expand (2x+4)^4 is 16x^4+128x^3+384x^2+512x+256