What is expand (1-2x)^5 ?

The solution to expand (1-2x)^5 is 1-10x+40x^2-80x^3+80x^4-32x^5

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expand (1-2x)^5

expand

(1 - 2 x)^{5}

1 - 10 x + 40 x^{2} - 80 x^{3} + 80 x^{4} - 32 x^{5}

Solution steps

(1 - 2 x)^{5}

Apply binomial theorem:

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

a = 1, b = - 2 x

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (- 2 x)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (- 2 x)^{0} : 1

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- 2 x)^{2} : 40 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- 2 x)^{3} : - 80 x^{3}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- 2 x)^{5} : - 32 x^{5}

= 1 - 10 x + 40 x^{2} - 80 x^{3} + 80 x^{4} - 32 x^{5}

(x^{50})^{2}

\frac{5 - 2 i}{7 + 3 i}

(- 0.6 m^{3} n^{2})^{3}

\frac{800}{3}

\frac{2}{x - 2} + \frac{x}{x + 9} - \frac{x + 20}{x ^{2} + 7 x - 18}

What is expand (1-2x)^5 ?
The solution to expand (1-2x)^5 is 1-10x+40x^2-80x^3+80x^4-32x^5