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Popular >

expand (e+4)^4

Solution

expand

(e + 4)^{4}

Solution

e^{4} + 16 e^{3} + 96 e^{2} + 256 e + 256

+1

Decimal Notation

2037.19627 \dots

Solution steps

(e + 4)^{4}

Apply binomial theorem:

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

a = e, b = 4

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

Expand summation

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

\frac{4 !}{0 ! ( 4 - 0 ) !} e^{4} \cdot 4^{0} = e^{4}

\frac{4 !}{1 ! ( 4 - 1 ) !} e^{3} \cdot 4^{1} = 16 e^{3}

\frac{4 !}{2 ! ( 4 - 2 ) !} e^{2} \cdot 4^{2} = 96 e^{2}

\frac{4 !}{3 ! ( 4 - 3 ) !} e^{1} \cdot 4^{3} = 256 e

\frac{4 !}{4 ! ( 4 - 4 ) !} e^{0} \cdot 4^{4} = 256

= e^{4} + 16 e^{3} + 96 e^{2} + 256 e + 256

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Frequently Asked Questions (FAQ)

What is expand (e+4)^4 ?
The solution to expand (e+4)^4 is e^4+16e^3+96e^2+256e+256