en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+4)^4

Solution

expand

(x + 4)^{4}

Solution

x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 256

Solution steps

(x + 4)^{4}

Apply binomial theorem:

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

a = x, b = 4

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 4^{1} : 16 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 4^{2} : 96 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 4^{3} : 256 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 4^{4} : 256

= x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 256

Popular Examples

factor 5x+15 factor

5 x + 15

simplify 7.4z-5(-1.6z+2.4)simplify

7.4 z - 5 (- 1.6 z + 2.4)

simplify \sqrt[3]{8x^3}simplify

3 8 x^{3}

simplify-1.5(4-n)+2.8 simplify

- 1.5 (4 - n) + 2.8

simplify-1/0 simplify

- \frac{1}{0}

Frequently Asked Questions (FAQ)

What is expand (x+4)^4 ?
The solution to expand (x+4)^4 is x^4+16x^3+96x^2+256x+256