What is expand (x+9)^4 ?

The solution to expand (x+9)^4 is x^4+36x^3+486x^2+2916x+6561

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+9)^4

expand

(x + 9)^{4}

x^{4} + 36 x^{3} + 486 x^{2} + 2916 x + 6561

Solution steps

(x + 9)^{4}

Apply binomial theorem:

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

a = x, b = 9

= i = 0 \sum 4 (i 4) x^{(4 - i)} \cdot 9^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 9^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 9^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 9^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 9^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 9^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 9^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 9^{1} : 36 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 9^{2} : 486 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 9^{3} : 2916 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 9^{4} : 6561

= x^{4} + 36 x^{3} + 486 x^{2} + 2916 x + 6561

\frac{45}{7} \cdot \frac{63}{125}

+ 4 x^{2} + 8 x y - x y - 2 y^{2}

(sin (x) - cos (x))^{2}

lo g_{3} (\frac{1}{3 3})

3 t^{2} - 18 t + 24

What is expand (x+9)^4 ?
The solution to expand (x+9)^4 is x^4+36x^3+486x^2+2916x+6561