en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1-x^2)^4

Solution

expand

(1 - x^{2})^{4}

Solution

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

Solution steps

(1 - x^{2})^{4}

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- x^{2})^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- x^{2})^{3} : - 4 x^{6}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- x^{2})^{4} : x^{8}

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

Popular Examples

simplify (2x^3-x^2-31x+35)/(2x-7)simplify

\frac{2 x ^{3} - x ^{2} - 31 x + 35}{2 x - 7}

simplify (-4-28i)/(-4-8i)simplify

\frac{- 4 - 28 i}{- 4 - 8 i}

expand (x+1)(3x^2-10x+8)expand

(x + 1) (3 x^{2} - 10 x + 8)

expand x(2x-5)expand

x (2 x - 5)

expand (7x+2)^2 expand

(7 x + 2)^{2}

Frequently Asked Questions (FAQ)

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