What is expand (1+2x)^6 ?

The solution to expand (1+2x)^6 is 1+12x+60x^2+160x^3+240x^4+192x^5+64x^6

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expand (1+2x)^6

expand

(1 + 2 x)^{6}

1 + 12 x + 60 x^{2} + 160 x^{3} + 240 x^{4} + 192 x^{5} + 64 x^{6}

Solution steps

(1 + 2 x)^{6}

Apply binomial theorem:

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

a = 1, b = 2 x

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (2 x)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (2 x)^{0} : 1

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (2 x)^{1} : 12 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (2 x)^{2} : 60 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (2 x)^{3} : 160 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (2 x)^{4} : 240 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (2 x)^{5} : 192 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (2 x)^{6} : 64 x^{6}

= 1 + 12 x + 60 x^{2} + 160 x^{3} + 240 x^{4} + 192 x^{5} + 64 x^{6}

6 (x + 1)

e^{a l n (x)}

- 11 + 8

- 12 + 1

- 12 - 1

What is expand (1+2x)^6 ?
The solution to expand (1+2x)^6 is 1+12x+60x^2+160x^3+240x^4+192x^5+64x^6