What is expand (a+3b)^4 ?

The solution to expand (a+3b)^4 is a^4+12a^3b+54a^2b^2+108ab^3+81b^4

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expand (a+3b)^4

expand

(a + 3 b)^{4}

a^{4} + 12 a^{3} b + 54 a^{2} b^{2} + 108 a b^{3} + 81 b^{4}

Solution steps

(a + 3 b)^{4}

Apply binomial theorem:

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

a = a, b = 3 b

= i = 0 \sum 4 (i 4) a^{(4 - i)} (3 b)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} a^{4} (3 b)^{0} : a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} a^{3} (3 b)^{1} : 12 a^{3} b

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} a^{2} (3 b)^{2} : 54 a^{2} b^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} a^{1} (3 b)^{3} : 108 a b^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} a^{0} (3 b)^{4} : 81 b^{4}

= a^{4} + 12 a^{3} b + 54 a^{2} b^{2} + 108 a b^{3} + 81 b^{4}

19 2^{2}

(10 - 10 i) - (10 + 7 i)

\frac{x ^{2} - ( x - 1 ) ^{2}}{x - 1}

- 9 x^{3} - 3 x^{2} + 3 x + 1

What is expand (a+3b)^4 ?
The solution to expand (a+3b)^4 is a^4+12a^3b+54a^2b^2+108ab^3+81b^4