What is expand (1-2x)^6 ?

The solution to expand (1-2x)^6 is 1-12x+60x^2-160x^3+240x^4-192x^5+64x^6

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expand (1-2x)^6

expand

(1 - 2 x)^{6}

1 - 12 x + 60 x^{2} - 160 x^{3} + 240 x^{4} - 192 x^{5} + 64 x^{6}

Solution steps

(1 - 2 x)^{6}

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 6 (i 6) \cdot 1^{(6 - i)} (- 2 x)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (- 2 x)^{0} : 1

Simplify

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

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (- 2 x)^{2} : 60 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (- 2 x)^{3} : - 160 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (- 2 x)^{4} : 240 x^{4}

Simplify

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

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (- 2 x)^{6} : 64 x^{6}

= 1 - 12 x + 60 x^{2} - 160 x^{3} + 240 x^{4} - 192 x^{5} + 64 x^{6}

\frac{8}{20}

2 \cdot 20

(x - 3) (2 x^{2} - 5 x + 1)

2 a^{2} x + 2 a x + 2 x - a^{2} - a - 1

\frac{4}{12} \cdot \frac{3}{11}

What is expand (1-2x)^6 ?
The solution to expand (1-2x)^6 is 1-12x+60x^2-160x^3+240x^4-192x^5+64x^6