What is expand (1-sqrt(x))^4 ?

The solution to expand (1-sqrt(x))^4 is 1-4sqrt(x)+6x-4xsqrt(x)+x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1-sqrt(x))^4

expand

(1 - x)^{4}

1 - 4 x + 6 x - 4 x x + x^{2}

Solution steps

(1 - x)^{4}

Apply binomial theorem:

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

a = 1, b = - x

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- x)^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- x)^{1} : - 4 x

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- x)^{3} : - 4 (x)^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- x)^{4} : x^{2}

= 1 - 4 x + 6 x - 4 (x)^{3} + x^{2}

Simplify

(x)^{3} : x x

= 1 - 4 x + 6 x - 4 x x + x^{2}

(x^{2} + 7 - 4) (x^{2} + 7 + 4)

(8 - 2 ln (x)) x

\frac{1}{( s ^{2} + 3 s + 2 ) ( s + 4 )}

(\frac{6}{x - 6} + 2 (100 - x)) (x - 6)

a (5, - 2) b (- 1, 2)

What is expand (1-sqrt(x))^4 ?
The solution to expand (1-sqrt(x))^4 is 1-4sqrt(x)+6x-4xsqrt(x)+x^2