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

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

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expand (3a+b)^4

expand

(3 a + b)^{4}

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

Solution steps

(3 a + b)^{4}

Apply binomial theorem:

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

a = 3 a, b = b

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(\frac{x}{2} + \frac{y}{3})^{3} - (\frac{x}{2} - \frac{y}{3})^{3}

- (0.01 - 0.05 x)

x^{2} - 6 + 4

(x^{2} - 3 y) (x^{3} - 5) + (x^{2} - 3 y) (y - x^{3})

\frac{x}{( x ( 1 + x ) )}

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