What is expand (1-x)^6 ?

The solution to expand (1-x)^6 is 1-6x+15x^2-20x^3+15x^4-6x^5+x^6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1-x)^6

expand

(1 - x)^{6}

1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

Solution steps

(1 - x)^{6}

Apply binomial theorem:

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

a = 1, b = - x

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (- x)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (- x)^{2} : 15 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (- x)^{3} : - 20 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (- x)^{4} : 15 x^{4}

Simplify

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

Simplify

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

= 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

3 + (- 9)

7 \cdot (- 7)

(9 + 8 i) (5 - 5 i)

\frac{3 !}{1 !}

(4)^{2} + (4)^{2}

What is expand (1-x)^6 ?
The solution to expand (1-x)^6 is 1-6x+15x^2-20x^3+15x^4-6x^5+x^6