What is expand (x+6)^4 ?

The solution to expand (x+6)^4 is x^4+24x^3+216x^2+864x+1296

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+6)^4

expand

(x + 6)^{4}

x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296

Solution steps

(x + 6)^{4}

Apply binomial theorem:

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

a = x, b = 6

= i = 0 \sum 4 (i 4) x^{(4 - i)} \cdot 6^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} \cdot 6^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} \cdot 6^{1} : 24 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} \cdot 6^{2} : 216 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} \cdot 6^{3} : 864 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} \cdot 6^{4} : 1296

= x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296

\frac{- 4}{- 5}

\frac{45}{28}

\frac{x y + 3 x z - 2 w y - 6 w z}{2 x y + w y + 3 w z + 6 x z}

418 \cdot 245 \cdot 75

\frac{3 ^{n + 1} + 3 ^{n + 2} + 3 ^{n + 3}}{3 ^{n - 1} + 3 ^{n - 2} + 3 ^{n - 3}}

What is expand (x+6)^4 ?
The solution to expand (x+6)^4 is x^4+24x^3+216x^2+864x+1296