What is expand (2a+b)^4 ?

The solution to expand (2a+b)^4 is 16a^4+32a^3b+24a^2b^2+8ab^3+b^4

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expand (2a+b)^4

expand

(2 a + b)^{4}

16 a^{4} + 32 a^{3} b + 24 a^{2} b^{2} + 8 a b^{3} + b^{4}

Solution steps

(2 a + b)^{4}

Apply binomial theorem:

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

a = 2 a, b = b

= i = 0 \sum 4 (i 4) (2 a)^{(4 - i)} b^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 a)^{4} b^{0} : 16 a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 a)^{3} b^{1} : 32 a^{3} b

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 a)^{2} b^{2} : 24 a^{2} b^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 a)^{1} b^{3} : 8 a b^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 a)^{0} b^{4} : b^{4}

= 16 a^{4} + 32 a^{3} b + 24 a^{2} b^{2} + 8 a b^{3} + b^{4}

\frac{28}{7}

(5 + 3 x)^{2}

\frac{5}{a} \cdot \frac{2 a}{b ^{2}} \cdot \frac{3 b}{10}

\frac{1}{x - 2}

- 3 + 12

What is expand (2a+b)^4 ?
The solution to expand (2a+b)^4 is 16a^4+32a^3b+24a^2b^2+8ab^3+b^4