What is expand (2x+6)^6 ?

The solution to expand (2x+6)^6 is 64x^6+1152x^5+8640x^4+34560x^3+77760x^2+93312x+46656

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2x+6)^6

expand

(2 x + 6)^{6}

64 x^{6} + 1152 x^{5} + 8640 x^{4} + 34560 x^{3} + 77760 x^{2} + 93312 x + 46656

Solution steps

(2 x + 6)^{6}

Apply binomial theorem:

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

a = 2 x, b = 6

= i = 0 \sum 6 (i 6) (2 x)^{(6 - i)} \cdot 6^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (2 x)^{6} \cdot 6^{0} : 64 x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 x)^{5} \cdot 6^{1} : 1152 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 x)^{4} \cdot 6^{2} : 8640 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 x)^{3} \cdot 6^{3} : 34560 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 x)^{2} \cdot 6^{4} : 77760 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 x)^{1} \cdot 6^{5} : 93312 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (2 x)^{0} \cdot 6^{6} : 46656

= 64 x^{6} + 1152 x^{5} + 8640 x^{4} + 34560 x^{3} + 77760 x^{2} + 93312 x + 46656

9 q + 1^{3}

8^{n + 2} \cdot 1 2^{n - 3}

(4 a^{- 2} \cdot b^{3})^{3}

4 (5 x - 8) + (- (- 8 x - 1))

(x + 4 y)^{3}

What is expand (2x+6)^6 ?
The solution to expand (2x+6)^6 is 64x^6+1152x^5+8640x^4+34560x^3+77760x^2+93312x+46656