What is expand (x+6)^4 ?

The solution to expand (x+6)^4 is x^4+24x^3+216x^2+864x+1296

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expand (x+6)^4

expand

(x + 6)^{4}

x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296

Solution steps

(x + 6)^{4}

Apply binomial theorem:

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

a = x, b = 6

= i = 0 \sum 4 (i 4) x^{(4 - i)} \cdot 6^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 6^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 6^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 6^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 6^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 6^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 6^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 6^{1} : 24 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 6^{2} : 216 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 6^{3} : 864 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 6^{4} : 1296

= x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296

- \frac{1}{2} \times 5

\frac{x}{x ^{2} - 2 x}

121 + 50

2 x^{3} y^{- 3} \times 2 x^{- 1} y^{3}

x^{2} - 5 x y^{2} + y^{3} - (8 x^{3} - y^{3})

What is expand (x+6)^4 ?
The solution to expand (x+6)^4 is x^4+24x^3+216x^2+864x+1296