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

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

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expand (2a+1)^6

expand

(2 a + 1)^{6}

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

Solution steps

(2 a + 1)^{6}

Apply binomial theorem:

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

a = 2 a, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

3 x^{2} \cdot 6 x

25 \div 25

24. 5^{2}

- k - 3 k^{2} + 5 k^{2} - 8 k

∣ 4 - 6 i ∣

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