What is expand (2-a)^5 ?

The solution to expand (2-a)^5 is 32-80a+80a^2-40a^3+10a^4-a^5

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expand (2-a)^5

expand

(2 - a)^{5}

32 - 80 a + 80 a^{2} - 40 a^{3} + 10 a^{4} - a^{5}

Solution steps

(2 - a)^{5}

Apply binomial theorem:

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

a = 2, b = - a

= i = 0 \sum 5 (i 5) \cdot 2^{(5 - i)} (- a)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 2^{5} (- a)^{0} : 32

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} (- a)^{1} : - 80 a

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 2^{3} (- a)^{2} : 80 a^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} (- a)^{3} : - 40 a^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} (- a)^{4} : 10 a^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} (- a)^{5} : - a^{5}

= 32 - 80 a + 80 a^{2} - 40 a^{3} + 10 a^{4} - a^{5}

\frac{22}{5} \div \frac{5}{11}

(3 x + 10) (2 x^{2} - 2 x + 3)

\frac{x ^{2}}{9} \cdot \frac{3}{x}

\frac{7 - x}{x - 7}

\frac{7}{x + 6} - \frac{x}{x ^{2} - x - 42}

What is expand (2-a)^5 ?
The solution to expand (2-a)^5 is 32-80a+80a^2-40a^3+10a^4-a^5