What is expand (2-x)^7 ?

The solution to expand (2-x)^7 is 128-448x+672x^2-560x^3+280x^4-84x^5+14x^6-x^7

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expand (2-x)^7

expand

(2 - x)^{7}

128 - 448 x + 672 x^{2} - 560 x^{3} + 280 x^{4} - 84 x^{5} + 14 x^{6} - x^{7}

Solution steps

(2 - x)^{7}

Apply binomial theorem:

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

a = 2, b = - x

= i = 0 \sum 7 (i 7) \cdot 2^{(7 - i)} (- x)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 2^{7} (- x)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 2^{6} (- x)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 2^{5} (- x)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 2^{4} (- x)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 2^{3} (- x)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 2^{2} (- x)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 2^{1} (- x)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 2^{0} (- x)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 2^{7} (- x)^{0} : 128

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} \cdot 2^{6} (- x)^{1} : - 448 x

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 2^{5} (- x)^{2} : 672 x^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 2^{4} (- x)^{3} : - 560 x^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 2^{3} (- x)^{4} : 280 x^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 2^{2} (- x)^{5} : - 84 x^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 2^{1} (- x)^{6} : 14 x^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 2^{0} (- x)^{7} : - x^{7}

= 128 - 448 x + 672 x^{2} - 560 x^{3} + 280 x^{4} - 84 x^{5} + 14 x^{6} - x^{7}

2 \frac{1}{2} \div \frac{1}{4}

\frac{0.9}{1 + \frac{1}{8}}

x^{6} \times x^{2}

\frac{4}{5} \times 4

x^{4} - 6 x^{3} + 13 x^{2} - 12 x + 4

What is expand (2-x)^7 ?
The solution to expand (2-x)^7 is 128-448x+672x^2-560x^3+280x^4-84x^5+14x^6-x^7