What is expand (x+h)^5 ?

The solution to expand (x+h)^5 is x^5+5x^4h+10x^3h^2+10x^2h^3+5xh^4+h^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+h)^5

expand

(x + h)^{5}

x^{5} + 5 x^{4} h + 10 x^{3} h^{2} + 10 x^{2} h^{3} + 5 x h^{4} + h^{5}

Solution steps

(x + h)^{5}

Apply binomial theorem:

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

a = x, b = h

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= x^{5} + 5 x^{4} h + 10 x^{3} h^{2} + 10 x^{2} h^{3} + 5 x h^{4} + h^{5}

- 6 x - 3 + 3 x - 9

x^{8} + 3 x^{4} + 4

- \frac{2}{3} p + \frac{1}{5} - 1 + \frac{5}{6} p

(d^{2} + 6 d + 9) + (d^{3} + 6 d + 9)

(x - 3 y)^{3}

What is expand (x+h)^5 ?
The solution to expand (x+h)^5 is x^5+5x^4h+10x^3h^2+10x^2h^3+5xh^4+h^5