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

The solution to expand (x^2-1)^5 is x^{10}-5x^8+10x^6-10x^4+5x^2-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x^2-1)^5

expand

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

x^{10} - 5 x^{8} + 10 x^{6} - 10 x^{4} + 5 x^{2} - 1

Solution steps

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

Apply binomial theorem:

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

a = x^{2}, b = - 1

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} (- 1)^{0} : x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (- 1)^{1} : - 5 x^{8}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (- 1)^{2} : 10 x^{6}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (- 1)^{3} : - 10 x^{4}

Simplify

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

Simplify

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

= x^{10} - 5 x^{8} + 10 x^{6} - 10 x^{4} + 5 x^{2} - 1

y^{2} - 3 y

3 \cdot 2 \cdot 1

\frac{16 x - 12}{4 x ^{2} + 5 x - 6} - \frac{3}{x + 2}

\frac{5}{- 6}

2 \frac{7}{10}

What is expand (x^2-1)^5 ?
The solution to expand (x^2-1)^5 is x^{10}-5x^8+10x^6-10x^4+5x^2-1