What is expand (2-x)^6 ?

The solution to expand (2-x)^6 is 64-192x+240x^2-160x^3+60x^4-12x^5+x^6

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expand (2-x)^6

expand

(2 - x)^{6}

64 - 192 x + 240 x^{2} - 160 x^{3} + 60 x^{4} - 12 x^{5} + x^{6}

Solution steps

(2 - x)^{6}

Apply binomial theorem:

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

a = 2, b = - x

= i = 0 \sum 6 (i 6) \cdot 2^{(6 - i)} (- x)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 2^{6} (- x)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 2^{5} (- x)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 2^{4} (- x)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 2^{3} (- x)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 2^{2} (- x)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 2^{1} (- x)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 2^{0} (- x)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 2^{6} (- x)^{0} : 64

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 2^{5} (- x)^{1} : - 192 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 2^{4} (- x)^{2} : 240 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 2^{3} (- x)^{3} : - 160 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 2^{2} (- x)^{4} : 60 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 2^{1} (- x)^{5} : - 12 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 2^{0} (- x)^{6} : x^{6}

= 64 - 192 x + 240 x^{2} - 160 x^{3} + 60 x^{4} - 12 x^{5} + x^{6}

x^{4} + 7 x^{2} + 12

32000

7 x^{3} (5 x - 3)

\frac{6}{7} + \frac{2}{9} + \frac{2}{5}

What is expand (2-x)^6 ?
The solution to expand (2-x)^6 is 64-192x+240x^2-160x^3+60x^4-12x^5+x^6