What is expand (x+8)^4 ?

The solution to expand (x+8)^4 is x^4+32x^3+384x^2+2048x+4096

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expand (x+8)^4

expand

(x + 8)^{4}

x^{4} + 32 x^{3} + 384 x^{2} + 2048 x + 4096

Solution steps

(x + 8)^{4}

Apply binomial theorem:

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

a = x, b = 8

= i = 0 \sum 4 (i 4) x^{(4 - i)} \cdot 8^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 8^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 8^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 8^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 8^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 8^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 8^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 8^{1} : 32 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 8^{2} : 384 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 8^{3} : 2048 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 8^{4} : 4096

= x^{4} + 32 x^{3} + 384 x^{2} + 2048 x + 4096

\frac{5}{2} \times \frac{5}{2}

+ 2 (\frac{48}{3})^{- \frac{1}{4}}

(3 x - 10) (3 x - 5)

2^{- 1 - 1}

2 \times (- x)

What is expand (x+8)^4 ?
The solution to expand (x+8)^4 is x^4+32x^3+384x^2+2048x+4096