What is expand (x+4)^5 ?

The solution to expand (x+4)^5 is x^5+20x^4+160x^3+640x^2+1280x+1024

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expand (x+4)^5

expand

(x + 4)^{5}

x^{5} + 20 x^{4} + 160 x^{3} + 640 x^{2} + 1280 x + 1024

Solution steps

(x + 4)^{5}

Apply binomial theorem:

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

a = x, b = 4

= i = 0 \sum 5 (i 5) x^{(5 - i)} \cdot 4^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} \cdot 4^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} \cdot 4^{1} : 20 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} \cdot 4^{2} : 160 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} \cdot 4^{3} : 640 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} \cdot 4^{4} : 1280 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} \cdot 4^{5} : 1024

= x^{5} + 20 x^{4} + 160 x^{3} + 640 x^{2} + 1280 x + 1024

(2 + 5 n^{2})^{2}

\frac{1}{s ^{2}} + 1

\frac{1}{8 !}

2 \times (- 7)

\frac{2}{3} \times (- 3)

What is expand (x+4)^5 ?
The solution to expand (x+4)^5 is x^5+20x^4+160x^3+640x^2+1280x+1024