What is expand (x+1)^7 ?

The solution to expand (x+1)^7 is x^7+7x^6+21x^5+35x^4+35x^3+21x^2+7x+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+1)^7

expand

(x + 1)^{7}

x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} + 7 x + 1

Solution steps

(x + 1)^{7}

Apply binomial theorem:

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

a = x, b = 1

= i = 0 \sum 7 (i 7) x^{(7 - i)} \cdot 1^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} \cdot 1^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} \cdot 1^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} \cdot 1^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} \cdot 1^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} \cdot 1^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} \cdot 1^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} \cdot 1^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} \cdot 1^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} \cdot 1^{0} : x^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} \cdot 1^{1} : 7 x^{6}

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} \cdot 1^{2} : 21 x^{5}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} \cdot 1^{3} : 35 x^{4}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} \cdot 1^{4} : 35 x^{3}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} \cdot 1^{5} : 21 x^{2}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} \cdot 1^{6} : 7 x

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} \cdot 1^{7} : 1

= x^{7} + 7 x^{6} + 21 x^{5} + 35 x^{4} + 35 x^{3} + 21 x^{2} + 7 x + 1

\frac{40}{16}

1 + (\frac{x}{1 - x ^{2}})^{2}

e^{0.01}

(a - 5) (a + 5)

3 \times 2

What is expand (x+1)^7 ?
The solution to expand (x+1)^7 is x^7+7x^6+21x^5+35x^4+35x^3+21x^2+7x+1